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USC Computer Science Technical Reports, no. 587 (1994)

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USC Computer Science Technical Reports, no. 587 (1994)

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Content Con tin uous Displa y of Presen tations Sharing Clips
Cyrus Shahabi and Shahram Ghandeharizadeh
Departmen t of Computer Science
Univ ersit y of Southern California
Los Angeles California Abstract
Databases w ere in tro duced to remo v e redundancy from con v en tional le systems to encourage shar
ing of information The same idea is extended in this study to supp ort sharing for con tin uous media
data t yp es ie video and audio Sharing in con v en tional databases results in up date anomalies when
information is mo died With presen tations mo vies sharing clips sequence of frames con tin uous
displa y b ecomes c hallenging as w ell T o ensure a con tin uous displa y a system should retriev e data at
a presp ecied rate Otherwise a displa ymigh t suer from disruptions or dela ys termed hiccupsT o
ensure a con tin uous displayusing a m ultidisk hardw are platform a video ob ject is strip ed in to a n um
b er of sub ob jects The system enforces a regular sc hedule on retriev al of eac h sub ob ject b y con trolling
the placemen t of the sub ob jects across the disks No w if dieren t presen tations share sub ob jects eac h
presen tation will enforce its o wn restrictions on the placemen t of the data This migh t result in irregular
sc hedules for alternativ e presen tations resulting in hiccups One approac h to this problem is to replicate
the shared sub ob jects as man y times as they app ear in dieren tpresen tations An alternativ e is to main
tain these sub ob jects memory residen t Due to readonly c haracteristic of the application f l ash memory
is appropriate for storing these sub ob jects These alternativ e approac hes result in dieren t storage costs
In this pap er wein v estigate eac h approachas w ell as a wide sp ectrum of h ybrid approac hes that minimize
the storage cost while ensuring a con tin uous displa y In addition this study in v estigates t w o alternativ e
paradigms to supp ort m ultiple users Demand and Data driv en In the former the displa yof a D A G
starts once a request references it In the latter all p ossible paths of a D A G are displa y ed p erio dical ly A price analysis is pro vided for eac h paradigm in order to congure the c heap est storage structure
In tro duction
Consider a datab ase consisting of a n um b er of digitized presen tations Eac h pr esentation consists of a
sequence of vide o clips where a clip is a sequence of fr ames Alternativ e presen tations migh t share clips
This sharing is curren tly demonstrated b y applications from the en tertainmen t industryF or example three
dieren tv ersions of the mo vie Clue w ere distributed eac h with a dieren t ending in order to main tain
the audiences susp ense Similarly m usic c hannels eg MTV VH pro duce sho ws where a single m usic
video clip is presen ted in eac h sho w at a dieren t time eg while the video clip migh t b e presen ted at the
b eginning of one sho w in a second sho w the same video migh t b e presen ted ten min utes in to the sho w
Figure a demonstrates dieren tv ersions of a mo vie conceptualized as a Directed Graph DG In this case
audiences after w atc hing the sequences a and b of video clips can p oten tially pro ceed to c d or e for three
dieren t endings Note that clips ha vev ariable sizes and hence v ariable durations F or example the displa y
of c migh t require min utes while the duration of d mightbe min utes The sequence f is the epilogue of
Av ersion of this pap er is to app ear in the A CM Multime dia Systems Journal This researc hw as supp orted in part b y
the National Science F oundation under gran ts IRI IRI NYI a w ard and CD A a HewlettP ac k ard
researc h gran t and a researc hgrantfromA TTNCRT eradata

a
b
c
d e
f
ending2
ending3
ending1
a. Alternative endings
b. Alternative ratings
a
b
f
cd e G
PG
PG-13 R
Figure Alternativ ev ersions
the mo vie A DG migh tha v e branc hes in the middle as w ell T o illustrate consider Figure b as a mo vie
with four dieren t ratings ie G PG PG R An adult audience ma y select to preview sequences c d and e while c hildren are restricted to only w atc h sequence c In general a DG migh tbe a com bination
of dieren t mo vies sharing man y clips
W e use the ob jectorien ted terminology in order to abstract out the structure of a presen tation
A mo vie
can b e view ed as a collection of video clips Eac h clip is an obj ect where ob jects ha vev ariable sizes clips
ha v e dieren t durations Moreo v er these ob jects are mem b ers of con tin uous media data t yp e and should
b e retriev ed and displa y ed at a presp ecied con tin uous rate T o illustrate a video ob ject based on NTSC
net w ork qualit y should b e retriev ed and displa y ed at a rate of megabits p er second m bps Has Lossy compression tec hniques can b e emplo y ed to reduce b oth the size of video ob jects and their bandwidth
requiremen ts see F o x for an o v erview A set of presen tations sharing ob jects are represen ted as a
Directed Graph DG Eac hv ertex in the graph represen ts an ob ject while an edge represen ts a link from
one ob ject to another Th us an ob ject ma y lead to sev eral dieren t ob jects and b e reac hed via dieren t
ob jects Eac h path of the DG corresp onds to a single presen tation Since w e exp ect nite presen tations
w e do not allo w cycles and fo cus on Directed Acyclic Graphs D A G Finite n um b er of lo ops in a cycle can
b e represen ted b y instan tiating eac h cycle in a D A G The user ma y select a path either b efore the displa y
ofaD A G has started termed staticor in teractiv ely while viewing a clip termed inter active T o separate
the storage manager whic h is the fo cus of this study from the user in terface this study concen trates on
static presen tations Ho w ev er to mak e the problem more c hallenging and in order to extend the solutions
for a sp ecial t yp e of in teractiv e presen tation in Section w eassumeno adv ance kno wledge ab out the users
decisions GivenaD A G a link from ob ject X to ob ject Y implies that the displayof Y should start
immediately after the displayof X ends This is iden tical to the me et temp oral relationship found in All T o simplify the problem this study considers only these t w o simple relations b y using a D A G to represen t
the database Ho w ev er the extension to supp ort other relations dened in All is straigh tforw ard This
is describ ed further in Section In this studyw e concen trate on the placemen t of a D A G on a hierarc h y of storage media in order
to guaran tee a con tin uous displa y for all the plausible paths of the D A G One approac h to store m ultiple
presen tations sharing ob jects clips is to replicate eac h clip as man y times as the clip app ears in dieren t
presen tations An alternativ e approachistomain tain the clip memory residen t Both approac hes migh t
result in storage space requiremen ts that is not economically justied Based on a n um b er of parameters
it migh t b e more appropriate to replicate some of the clips while storing others in memory a com bined
approac h Moreo v er it migh tbe c heap er to store or replicate a p ortion of a clip on magnetic disk
driv es while the rest resides in memory a h ybrid approac h In eac h case the system should ensure a
con tin uous displa y for all the presen tations sharing those ob jects This study in v estigates alternativeobject
The terms mov ie and pr esentation are used as synon yms in this pap er

placemen t strategies in order to satisfy t w o ma jor ob jectiv es First guaran tee acon tin uous displayofall
the presen tations in a database Second minim izing the cost of storage space required b y the database
Wein v estigate t w o alternativ e paradigms for displa ying a D A G Demand and Data driv en With the
demand driv en paradigm the system displa ys a presen tation when a user references that presen tation An
example of this paradigm is our ev eryda y use of a V CR device Using this device a user displa ya mo vie
whenev er desirable Its primary adv an tage is a lo w latency time Ho w ev er in a m ultiuser en vironmen t
to main tain the lo w latency time there should b e a onetoone relationship b et w een the activ e users and
a v ailable resources one V CR p er user If the n um b er of resources is less than the n um b er of activ e requests
then a queue of p ending requests is formed causing eac h queued request to observ e a latency time The
a v erage latency is dep enden t on the displa y time of the ob ject referenced byeac h request and the n um ber
of p ending requests
With the data driv en paradigm the data is retriev ed and displa y ed p erio dicallyThe p ay p er view c able
servic e is an example of this paradigm A single mo vie is displa y ed p erio dically sa y once ev ery t w o hours
regardless of the n um b er of requests This paradigm ma y suer from a high a v erage latency time maxim um
of t w o hours observ ed b y those requests arriving after the displa y has started Ho w ev er a single resource
a cable c hannel in this example is sucien t to service a large n um b er of users theoretically an innite
n um b er of users
T o reduce the latency time in this paradigm one can increase the n um b er of resources
eg t wocable c hannels and displa y the mo vie with dieren t starting time sa y one hour apart on eac h
c hannel In this case the user observ es a one hour latency time byswitc hing c hannels W e describ e the
placemen t of the ob jects in a D A G for eac h paradigm that realizes b oth of our ob jectiv es
Recen tlyan um b er of studies ha vein v estigated retriev al of presen tations consisting of con tin uous media
in order to supp ort their hiccupfree displa y BGMJ AH R VR R V CL TPBG R W W e
will extend one of the prop osed tec hniques namely simple striping BGMJ to supp ort a hiccupfree
display ofaD A G T o realize a system that is economically viable these studies ha v e fo cused on a storage
hierarc h y that consists of dynamic random access memory DRAM and magnetic disk storage DRAM
pro vides a short latency time t ypically nanoseconds a high bandwidth megab ytes p er second
for Sync hronous DRAM PNHV and is fairly exp ensiv e p er megab yte of storage at the time of
this writing Magnetic disk driv es are mec hanical devices that pro vide a c heap form of storage p er
megab yte of storage Ho w ev er up on the arriv al of a request they incur a high latency time t ypically to milli seconds and pro vide a lo w bandwidth to megab ytes p er second W e extend this hierarc h y
with solid state memory DH termed f l ash due to b oth its increased p opularit y and suitabilit y of its
ph ysical c haracteristics to this application Flash memory pro vides a transfer rate and a latency time almost
iden tical to DRAM It diers from DRAM as follo ws it is c heap er is suitable for readonly data
the write op erations on ash are slo w moreo v er they slo wdo wn the read p erformance of this medium if
p erformed frequen tly
As compared to magnetic disk storage the lo w latency of ash with to nanoseconds readaccesstime DH and its high transfer rate allo w it tobem ultiplexed among m ultiple
requests for data retriev al while ensuring a con tin uous displa y for eac h request The readonly c haracteristic
of a presen tation render the use of ash memory attractiv e
In this pap er w e rep ort p erformance results on neither a hiccupfree displa y noralo w storage cost As far
as the rst ob jectiv e is concerned the designs are constructed using simple striping As sho wn in BGMJ the placemen t of ob jects using simple striping guaran tees a hiccupfree displa yF or the second ob jectiv e w e
prop ose analytical mo dels that quan tify the storage cost based on the c haracteristics of an application and
system parameters These mo dels can b e emplo y ed for a v ariet y of applications The results obtained for
one application is sp ecic to that application and cannot b e generalized to others
There are other dierences b et w een the t w o paradigms suc h as the abilit y to con trol the displa y eg fast forw ard These
features do not constitute the fo cus of this study Note that DRAM cannot b e replaced with ash b ecause the data m ust b e temp orarily staged somewhere b efore its displa y using ash for this purp ose is a mistak e b ecause frequen t write op erations to this medium renders it useless

Sub ob ject a strip e of an ob ject It represen ts a con tiguous p ortion of the ob ject Its
size is determined at system conguration time
D A G a Directed Acyclic Graph used to presen t a database of presen tations
sharing clips
Channel A fraction of a v ailable disk bandwidth required to displa y an ob ject
Platform aph ysical storage with sucien t bandwidth to supp ort the displayofat
least one sub ob ject
Time In terv al The duration of time required to displa y a sub ob ject from a c hannel
T able Dening terms
Ov erview
Placing a com bination of dieren t ob jects with dieren t bandwidth requiremen ts forming a directed graph
on a m ultidisk en vironmen t is an op en researc h area In this pap er the follo wing assumptions are made to
simplify the problem
A directed graph has no cycles ie Directed Acyclic Graph D A G
A D A G has a single sour ce In practice this can b e ac hiev ed b y adding a common title to the b eginning
of anyD A G Note that this assumption is made to simplify the description of the tec hniques In general
a user can displa y a presen tation starting from an y of its ob jects
W e concen trate on a single D A G F or m ultiple D A Gs if they do not share ob jects then eac h of them
can b e considered separately Otherwise an articial sup er sour c e is used to reduce the problem to a
single D A G
Bandwidth required to displa y an ob ject remains unc hanged during its displa y Bandwidth required to displa y eac h ob ject in a D AGisiden tical If this is not true stagger e d strip
ing BGMJ should b e emplo y ed instead of simple striping This has no impact on the prop osed
solutions and cost functions
The b ottlenec k resource is the disk subsystem W e assume that the bandwidth of b oth the net w ork
and connection buses is signican tly higher than the bandwidth of the disk subsystem
Price p er megab yte of ash memory is lo w er than that of DRAM W al otherwise replace ash with
DRAM
The fo cus is to displa y a presen tation consisting of video ob jects F eatures suc h as pause fastforw ard
and rewind constitute our future researc h direction
No w consider the display ofaD AGwith eac h of the demand and data driv en paradigms With the
demand driv en paradigm although a single resource p er activ e request is still sucien t to displaythe D A G
an umberofactiv e requests arriving at the same time cannot b e group ed together This is b ecause eac h
user migh t elect to view a dieren t presen tation pursuing a dieren t path Ob viously this is imp ossible in
the presence of a single resource V CR Hence the n um b er of activ e requests is a function of the a v ailable
bandwidth and a fraction of the bandwidth required b y eac h request otherwise a latency time is observ ed
This latency time is indep endentof the n um b er of alternativ e paths in the D A G and is a function of the
displa y time of the D A G and the n um b er of p ending requests Similarly emplo ying the data driv en paradigm
requires more resources to displayaD A G as compared to that of a single mo vie Consider a D A G with p
alternativ e paths T o displa y this D A G sa yin a pa y p er view cable service p cable c hannels resources are
required eac h to displa y one path Note that the maxim um latency time is no w the duration of the longest

Figure Logical c hannels in simple striping
path Max D ispl ayof the D A G One ma y reduce the latency time b y increasing the n um b er of resources
asam ultiple of p In order to describ e the details of these t w o paradigms w e need to fo cus on a tec hnique that retriev es video
and audio ob jects in a manner that supp orts its con tin uous displa yW eha v e elected to fo cus on simple
striping This tec hnique minim izes the amoun t of memory required to displa y an ob ject b y establishing a
pip eline b et w een the magnetic disk driv es and a displa y station Since the bandwidth of the disk driv es
is the b ottlenec k resource it partitions the aggregate bandwidth of the a v ailable disks in to R c hannels
C
C
C
R
in order to supp ort R sim ultaneous displa ys In order to distribute the load of a displa y
referencing an ob ject x across the c hannels it strip es ob ject x in to
size x size subobj ect sub ob jects and assigns the
sub ob jects of x to the c hannels in a roundrobin manner The size of eac h sub ob ject is xed for all ob jects
and determined at system conguration time
T o illustrate in Figure a sub ob jects of x x
x
x
are assigned to an c hannel system starting with C
T o ensure a con tin uous displa y the bandwidth
This size dep ends on system a v ailable memory size magnetic disk driv ec haracterist ics and some other factors whic his
bey ond the scop e of this pap er

ofac hannel should b e equal to the displa y bandwidth of the ob jects B
D isplay
minim izing the amoun t
of memory required b y pip elining the data from the disk to a displa y Hence denoting the eectiv e disk
bandwidth considering the maxim um seek and latency time see BGMJ with B
Disk
if M B D isplay
B D isk
then the n um ber of c hannels R is computed as
R D
M
where D is the n um b er of disk driv es Moreo v er R determines the n um b er of sim ultaneous requests supp orted
b y the system
When M eac hc hannel pro vides a fraction of a disk bandwidth see Figure a If M then
eac h sub ob ject is declustered GRA Q in to M fragmen ts and the aggregate bandwidth of M disk driv es
determine the required bandwidth of a c hannel see Figure b In Figure b x
ij
represen ts the j th
fragmen t of the ith sub ob ject of xT o ensure a con tin uous display ofanobject x the displa y of a fraction
of x
i
is o v erlapp ed with the retriev al of a p ortion of x
i for details see BGMJ The duration of the
retriev al of a sub ob ject is xed for all sub ob jects regardless of their media t yp e and is termed a Time
In terv al When the system displa ys x it emplo ys a single c hannel during eachtime in terv al Hence the
maxim um n um ber of a v ailable Time In terv als is equal to the n um ber of c hannels and denes the maxim um
n um b er of displa ys that can b e supp orted sim ultaneously R Eac h displa y iterates o v er the a v ailable
c hannels emplo ying eac h in a roundrobin manner in order to distribute its w ork ev enly across the c hannels
The roundrobin sc heduling of c hannels a v oids m ultiple requests from colliding with one another once their
displa y has b een initiated T o illustrate in Figure a assume a time in terv al that corresp onds to C
is
a v ailable Emplo ying that in terv al x
can b e displa y ed In the next in terv al the system emplo ys C
to
retriev e and displa y x
This pro cess rep eats itself un til x is displa y ed en tirelyA t the same time R other in terv als can b e utilized to service R other requests Therefore to displa y x assuming only one
time in terv al is a v ailable in the w orst case R Time Interval seconds are required un til the idle
in terv al reac hes C
where Time I nter v al is the duration of a time in terv al in seconds
Let a pl atf or m dene a ph ysical storage with sucien t bandwidth to displa y at least one sub ob ject
F or example in Figure a a platform consists of a single disk driv e while in Figure b a cluster of four
disk driv es constitute a platform When M there is a onetoone relationship b et w een a platform and
ac hannel This relationship is onetoman y when M F or instance in Figure a where M a
sub ob ject placed on platform can b e displa y ed from C
C
C
and C
whereas in Figure b where
M x
whic h is placed on platform can only b e displa y ed from C
F or the rest of this pap er w e assume
M This assumption is made not to simplify the problem but to consider the situation whic hin tro duces
the most c hallenging problems T o observ e lets illustrate the placemen tofaD A G with simple striping
In Figure b oth D A Gs consist of three ob jects x y and z where eac h has a dieren t size Figure a
demonstrates the placemen t of a simple D A G for a system that consists of eightc hannels R In this
case a time in terv al mightbe reserv ed b y a user sa y U
xy
who decides to displa y y after x path xy
Another user ma y desire to displa y z after x U
xz
T oa v oid hiccups for either user once the displa yof x is
complete the rst sub ob ject of b oth y and z are placed on the c hannel follo wing the one that con tains the
last sub ob ject of xHo w ev er this ma y not b e p ossible for all D A Gs F or example the extended D AGof
Figure b is dened suc h that users are allo w ed to displa y z after b oth x and yIf z starts from C
see the
rst placemen t in Figure b a user c ho osing path xy z migh t observ e a hiccup b ecause the regular sc hedule
of simple striping dictates that this displa y emplo ys C
while the displa y needs C
to satisfy the user and
C
migh t b e busy servicing other users On the other hand if the displa yof z starts from C
see the second
placemen t in Figure b then a user c ho osing path xz mightobserv e a hiccup b ecause another request migh t
b e using C
when the curren t request is done with the displayof x
using C
Hence to b e able to sc hedule
either time in terv als emplo y ed b y U
xy z
or U
xz
regularly in order to displa y z imm ediately after x or yit
should b e p ossible to displa y z
using b oth C
and C
If M C
and C
corresp ond to t w o dieren t
platforms due to a onetoone relationship requiring z
to b e placed on b oth platforms
Ho w ev er when
Due to this constrain t one migh t replicate z
t wice on the t w o platforms This strategy and some other alternativ es are
discussed in Section
Figure Placemen tof D A G with simple striping
M C
and C
migh t b oth corresp ond to a single platform sa y P
i
as in Figure a Hence placing
z
on P
i
will simply ensure con tin uous displa y of the D A G indep enden t of users decision Note that if C
and C
corresp ond to t w o dieren t platforms then the problem w ould b e iden tical to the case when M
Since problems for M is a subset of problems for M the tec hniques describ ed in this study can b e
applied to M as w ell Ho w ev er taking adv an tage of the exibilities of M the prop osed tec hniques
can b e optimized further F or example one migh t rst detect if t w o dieren tc hannels corresp ond to a single
platform If so then there is no constrain t on ob ject placemen t otherwise the problem is solv ed similar to
the case when M W e consider these optimizations as implemen tation tec hniques and will not consider
M an y further Ho w ev er if a single disk is partitioned in to regions or zones restricting the assignmen t
of an ob ject on a single disk driv e in order to reduce the seek time or maxim ize the utilization of the disk
bandwidth GKS GKS the problem for M b ecomes equiv alent tothatof M
Since there is alw a ys a onetoone relationship b et w een a platform and a c hannel when M the terms
channel and platform are used in terc hangeably for the rest of this pap er Hence w euse C
i
for b oth c hannel
i and the platform corresp onding to c hannel i Our prop osed solutions to the ab o v e problem include in telligen t placemen t of the ob jects replication
using DRAM as a staging area and main taining a p ortion of ob jects ash residen t The most trivial solution is
to replicate the ob ject as man y times as it app ears in a path An alternativ e is to use ash memory The read
only c haracteristic of the application encourages the use of ash memory due to its ph ysical c haracteristics
as discussed in Section The ash memory is used to store the rst p ortion of an ob ject termed head while the rest resides on the disks In this case indep enden t of the lo cation of the free in terv al the displa y
of the ob ject starts imm ediately Mean while the free in terv al is emplo y ed to retriev e the rest of the ob ject
that is disk residentin to the DRAM Once the displa yof head ends enough data is accum ulated in DRAM
in order to ensure a hiccupfree displa yT o reduce the amoun t of ash and DRAM requiremen t ob jects
should b e placed in telligen tly on the disk c hannels In order to decrease the total storage cost further a
com bination of replication and ash residen t p ortion migh t b e appropriate In this pap er these alternativ es
are in v estigated in detail for b oth the demand and data driv en paradigms
The rest of this pap er is organized as follo ws Section describ es the demand driv en paradigm It
in tro duces four alternativ e ob ject placemen t strategies and pro vides a price analysis in order to c ho ose the

C
C
C
C
C
C
C
C
u
k
v
l
w
m
T able The placemen t of the last sub ob jects of u v and w in an c hannel system
c heap est alternativ e The data driv en paradigm is describ ed in Section It demonstrates that the same
placemen t strategies can b e emplo y ed here with some mo dications In Section the t w o paradigms are
compared with eac h other and a system that com bines the t w o paradigms are discussed The option of
main taining a D AGen tirely ash residen t is also briey in v estigated Section concludes this pap er and
lists our future researc h directions
Demand Driv en P aradigm
With the Demand Driven p ar adigm once a request arriv es an empt y time in terv al is assigned to that request
The request o ccupies this time in terv al for the en tire displa y time of the users desired path Therefore in a R
c hannel system at most R requests can b e serviced sim ultaneously
The R th request should w ait un til
a time in terv al dedicated to an activ e request b ecomes a v ailable the activ e request terminates resulting
in the w orst latency time of Max Display the duration of the longest path
If the n um b er of requests in
ev ery Max D ispl ay seconds exceeds R a request queue is formed and the latency time b ecomes a function
of the n um b er of p ending requests and Max D ispl ay This paradigm is indep enden t of the complexityof
the D A G That is once a time in terv al is assigned regardless of the n um b er of alternativ e links c hosen b y
the user that same in terv al is sucien t to complete the user request Moreo v er this paradigm is appropriate
when the n um b er of requests during Max D ispl ay is less than or equal to R and the D A G is complex
Ob ject PlacementF or Demand Driv en
With this paradigm similar to the discussion of Section the placemen t of eac h ob ject of the D A G
dep ends on the placemen t of its predecessors T o illustrate assume that a tra v ersal from three
alternativeobjects u v and w leads to ob ject x ie u v and w are the three predecessors of x The
last sub ob ject of u v and w reside on three dieren tdisk c hannels C u
k
C v
l
and C w
m

resp ectiv ely see Figure a and T able The ob jectiv e istoplace x in telligen tly in order to ensure regular
sc heduling for all three paths ux vxand wx A complete D AG isacom bination of ob jects Eac h ob ject migh t b e replicated ha v e a p ortion in
ash b e en tirely ash residen t or b e replicated and ha v e a p ortion in ash F or ob ject x of the D A G
in Figure a consider eac h strategy in turn Section pro vides a complete algorithm to tra v erse a D A G
ob ject b y ob ject and place eachobjectbyc ho osing one of the follo wing strategies based on a price analysis
Replication
One alternativ e is to replicate x three times see Figure b and T able In this case the n um ber of
copies required for an ob ject x is not fan in xn um b er of incoming edges to x instead it is path in x Note that if some n um b er of users request an iden tical path they can b e group ed together In this study ho w ev er w e
assume no prior kno wledge ab out the user c hoice
Note that in the w orst case the activ e request migh t b e referencing the longest path

Figure Alternativ e ob ject placemen t
C
C
C
C
C
C
C
C
u
k
v
l
w
m
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
T able Replication x is replicated three times
n um b er of paths from sour ce of the D AGto x This explains wh y b oth ob jects x and y should b e copied
path in y times instead of just once fan in y Note that path in x denes the maxim um
required n um b er of copies The reason is that the last sub ob ject of b oth u and v migh t reside on the same
c hannel ie C u
k
C v
l
Moreo v er if x has R copies eac h should start from a dieren tc hannel then
indep endentof path in x all paths to x canbesc heduled regularly Hence the maxim um n um b er of replica
of x is b ounded b y Min R path in x
Readahead Buering
W e start b y pro viding a general idea of this tec hnique Subsequen tlyw e formalize its details The general
concept is as follo ws Supp ose x is placed after u see T able and x
x
are p ermanen tly staged in
ash memory No w consider path vx once the displayof v is nished and the time in terv al corresp onding
to C
b ecomes a v ailable The system uses the free time in terv al to readahead x
in to DRAM and at the
same time displa y x
from ash memory see Figure In the next in terv al the system readsahead x
in to DRAM and displa ys x
from ash This pro cess is rep eated un til the time in terv al corresp onding to C
b ecomes a v ailable time in Figure A tthispoin t the system displa ys x
from DRAM and readsahead
C
C
C
C
C
C
C
C
u
k
v
l
w
m
x
x
x
x
x
x
x
x
x
T able Readahead Buering Only one cop yof x paths vx and wx require to readahead x
Figure Readahead Buering sc hedule
x
in to DRAM After that nothing is retriev ed from the disk c hannels for four time in terv als they are either
idle or emplo y ed b y a nonrealtime request The displa y of the next ob ject for this request emplo ys C
due to the regular sc hedule requiring the system to shift one c hannel to the righ t during eac h time in terv al
regardless of whether they are emplo y ed or not One migh t b e tempted to start the placemen t of the next
ob ject sa y y from C
and instead of rendering c hannels idle during the shrinking state utilize them to
retriev e yHo w ev er this is not p ossible b ecause w e assumed no adv ance kno wledge ab out the user decision
Therefore the iden tit y of the next ob ject is unkno wn it migh tbe either y or some other ob ject Besides
placing y on C
migh t b e b enecial for path vxy but not for wxy whichis alsoa v alid path
During a displa y the readahead buering impacts the con ten ts of DRAM the con ten ts of ash is pre
determined during the system placemen t of the ob ject and remains unc hanged The DRAM requiremen ts of
a displa y has three states a gro wing state a steady state and a shrinking state see Figure Let head
i
v x denote the n um b er of sub ob jects of x required to b e ash residen t for path vx when x
resides on C
i
in
this example head
v x head
i
v x denes b oth the maxim um n um b er of sub ob jects required to b e
DRAM residen t DRAM is stable at head
i
v x sub ob jects and the n umberoftime in terv als during whic h
the c hannel is not emplo y ed see Figure The n um ber of time in terv als DRAM is in steady state stable
in terv als can b e computed as size x head
v x The same idea can b e rep eated for ob ject wHo w ev er since x
resides on C
ie C w
m
C x
head
w x will b e Hence the n um b er of sub ob jects of x that should b e ash residen tis Max head
v x head
w x H
x Note that once w eha v e H
x sub ob jects of x ash residen t
it is no longer necessary to main tain them on disk Hence the n um b er of sub ob jects of x that b ecome disk
residen t is reduced to
disk space size x H
x Similar to the discussion of Section H
i
x is b ounded b y R H
i
x R That is once
R sub ob jects of x b ecome ash residen t indep enden tof the c hannel con taining the last sub ob ject of its
predecessors the sc heduling of all the incoming paths to x can b e done regularly With demand driv en in the w orst case there are R sim ultaneous requests for an ob ject x where the
memory migh t b e in steady state for all of them T o illustrate assume R and head t z and
size z Hence for path tz memory is stable at sub ob jects for time in terv als

Figure Computation of optimal head size
Supp ose dieren t requests to z the rst one requires z
to z

b e DRAM residen t the second requires
z

to z
b e DRAM residen t and nally the last requires z

to z

b e DRAM residen t Th us totally
R head t z memory pages the size of eac h page is equiv alen t to the size of a sub ob ject of DRAM
is required this is the w orst case scenario that results in maxim um DRAM requiremen t Ho w ev er if
size z H
i
z R H
i
z then in the w orst case z will b ecome memory residentin its en tirety H
i
zin
ash and the rest in DRAM Hence the maxim um amoun t of required DRAM is
max dr am Min R H
i
z size z H
i
z In practice instead of k eeping readahead sub ob jects in DRAM during the gro wing and steady state a
dynamic sc heduler can emplo y idle in terv als to ush them on to the disk In this case they can b e retriev ed
later byemplo ying other idle in terv als F or example in Figure consider time when the system is retrieving
x
from C
see T able Supp ose the time in terv al corresp onding to C
is free x
can b e ushed on to
C
to free up DRAM Later at time during the shrinking state instead of rendering a time in terv al
idle to displa y x
from DRAM the time in terv al can b e utilized to retriev e x
from C
C
w as selected to
resp ect the regularit y of the displaysc hedule In general the duration of time from when x
l
becomes DRAM
residentun til it is displa y ed is dened as H
i
x time in terv als In the b est case if x
l
is readahead from
C
k
at time t it can b e ushed immediately to C
k H i x mo d R in order to b e retriev ed and displa y ed
later at time t H
i
x Observ e that retriev al do es not alw a ys o ccur during the shrinking state Hence the
existence of an idle in terv al to b e utilized for retriev al is not alw a ys guaran teed Therefore to ac hiev e the
b est case scenario the sc heduling should b e done dynamically and in telligen tlyT o illustrate assume at time
x
is retriev ed from C
and ushed on to C
C
mo d Ho w ev er at time H
i
x the idle
in terv al corresp onding to C
is emplo y ed to retriev e x
and not x
A t this p oin t the system should retriev e
x
and p ostp one the retriev al of x
F urthermore it should guaran tee that the time in terv al corresp onding
to C
will b ecome a v ailable no later than time to retriev e x
This tec hnique is called Dynamic Sub obje ct
Shuing and it is useful to reduce the DRAM requiremen t when the system is underutilized the n um ber
of activ e requests is smaller than R Note that since this pro cess is dynamic to congure the system the
w orst case DRAM requiremen t ie Min R H
i
x size x H
i
x should still b e considered
Minim um Head
H
i
x should b e minim ized for eachobject x in the D A G in order to reduce the amoun t of required ash
and DRAM The problem is ho w to place ob ject x in a R c hannel system suc h that it results in minim um
head for x More sp ecically whic hc hannel should con tain the rst sub ob ject of x Consider edges u x
v x z xin a D A G If x is placed starting with c hannel one then it will ha v e the follo wing head sizes
for alternativ e paths head
u x head
v x head
z x see Figure F or that placemen t H
x will b e the maxim um of the ab o v e sizes W e can rep eat this pro cedure for eachc hannel i where i R to determine the c hannel j that minim izes H
i
x denoted as the optimal he ad size H x The complexit y
of the ab o v e optimal algorithm is O path in x R for eac hobject of the D A G T able illustrates the

i head
i
u x head
i
v x head
i
w x H
i
x T able A table to compute the optimal head size of x H x in thisexample C
C
C
C
C
C
C
C
u
k
v
l
w
m
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
T able Readahead Buering and Replicate x is replicated t wice path wx requires to readahead x algorithm to nd H x for the example in Figure a
App endix A demonstrates ho w the complexit y of the algorithm can b e signican tly reduced to
O log fan in x fan in x
Readahead Buering and Replication
The idea is to b oth replicate an ob ject and k eep its head ash residen t This reduces the size of the head
of x ev en further in order to minim ize the required amoun t of b oth ash and DRAM see Figure c and
T able F or example b y eliminating the rst column of T able the optimal head size of x H x is no w reduced to sub ob jects Note that this reduction is also adv an tageous for H y see Equation in
App endix A ho w ev er it increases fan in y see Figure c
Flash Residen t
An alternativ e approac h to all the ab o v e strategies is to main tain the en tire ob ject ash residen t This
placemen t needs neither DRAM nor disk storage In tuitiv ely for those ob jects that their optimal head size
are appro ximately equal to their en tire size this placemen t will b e sup erior
A Price Analysis to Cho ose the Cheap est Placemen t Strategy
T o decide whic h of the ab o v e placemen t options to c ho ose from w epro vide a comparison strategy There
are man y factors that inuence a nal c hoice the size of the ob ject its fan in its path in and its optimal

head size as w ell as arc hitectural factors suchas n um ber of c hannels Rand the a v ailable DRAM and ash
memory Assume disk ramand f l ash are the price p er megab yte of disk ash and DRAM storage resp ec
tiv ely Moreo v er assume n is the n um b er of copies of an ob ject x on disk where n Min path in x R
Hence
n ash residen t
n Readahead Buering
n Min path in x R Replication
n other w ise Readahead Buering
and Replication
The ob jectiv e is to nd the b est v alue of n in order to minim ize the price of storage Note that H xis
c hanging for dieren tv alues of nhence Hx n optimal head size of x when x has n copies on disk is used
instead where
Hx Min path in x R Hx size x The follo wing denes the price for eac h resource as a function of n The disk price is computed using
Equation as
disk pr ice n n size x Hx n disk Since the required amount of ashisiden tical to the optimal head size
flash pr ice n Hx n f l ash The required amoun t of dram from Equation is
dr am n Min R Hx n size x Hx n Ho w ev er assuming Mem is the amoun t of memory required b y the ob jects assigned th us far the amoun tof
extra DRAM required b y the assignmentof a new object x is
E xtr a Mem n
If dr am n Mem
dr am n Mem otherwise
Hence
ram pr ice n E xtr a Mem n ram
The amoun t of required Mem is no w up dated to b e
Mem Mem Extra Mem n
The v alue of n for eac h ob ject is determined in order to minim ize stor ag e pr ice n where
storage pr ice n
disk pr ice n flash pr ice n ram pr ice n
Figure is a greedy algorithm
for ob ject placemen t in the Demand Driv en paradigm The reason that
the algorithm is greedy is b ecause it starts from sour ce and place the ob jects indep enden t of their successors
as it tra v erses the D A G Figure denes the Place subroutine used in Figure The input to the algorithm
is a D A G G V E and R where V and E are the sets of the D A Gs v ertices and edges resp ectiv ely W e b eliev e this is also an optimal algorithm In App endix A w e informally pro v ed the optimalit y of the greedy algorithm
using fan in instead of path in for readahead buering W e exp ect this to b e true when the com binatio n of strategies are
emplo y ed Ho w ev er w e do not as y et ha v e a pro of

Mem x sour ce
P LAC E D while V PLACED P l ace x P LAC E D P LAC E D f xg
Cho ose an ob ject x from V PLACED suc h that all the predecessors
of x are in PLAC E D
END
Figure The main placemen t algorithm
Algorithm in Figure migh t execute lines and for the rst series of the ob jects b ecause of the
initial v alue of Mem that migh t result in a high v alue of ram price Ho w ev er later in the D A G other ob jects
migh t increase MemIt w ould b e adv an tageous for the starting ob jects to tak e adv an tage of this price pa y ed
memory this can b e ac hiev ed b y rerunning the algorithm with the v alue of Mem pro duced from the rst
run
Data Driv en P aradigm
A limitati on of the demand driv en is that once the n um b er of users exceeds the n um ber of a v ailable resources
R the latency time increases as a function of n um b er of the p ending requests T oa v oid this for D A Gs
with a few paths w ein v estigate the Data Driven p ar adigm With this paradigm eac htime in terv al is
assigned to eac h p ossible path This is iden tical to the p ay p er view c able servic e analogy where eac h cable
c hannel w as assigned to a single path Hence for a D AGwith p p ossible paths at least p time in terv als
are required Recall from Section that R p c hannels are required to pro vide the system with p time
in terv als F urthermore to reduce the latency time again similar to pa y p er view analogy the n um ber of
in terv als m ust increase as a m ultiple of p Therefore k groups of p time in terv als are dedicated to displa y
all p ossible paths of a D A G p erio dically In this case in theory an innite n um b er of users can b e group ed
together and emplo y one of the k groups of displa ys If a request arriv es once the displa y of a group has b een
initiated it m ust w ait un til the next p erio d when the system starts to displa y the next group Therefore
the larger the v alue of kthe lo w er the latency time Ho w ev er the lo w er b ound for the w orst latency time
is p time in terv als This is b ecause a maxim um of p time in terv als are required un til the time in terv al
corresp onding to the c hannel con taining the rst sub ob ject of the source of the D A G b ecomes a v ailable
Moreo v er the longer Max D ispl ay the higher the v alue of k should b e to reac h the lo w er b ound of p time
in terv als latency time Since R k p the more complex the path large p and Max Display the more
c hannels R are required to reduce the latency time While the maxim um latency time cannot b ecome less
than p time in terv als This paradigm is appropriate when the n um b er of requests in ev ery p time in terv als
exceeds p and the application can tolerate p time in terv als latency time
The maxim um latency observ ed b y a user b efore the displayofthe D A G starts is in terv als
Max p M ax D ispl ay R p
where the unit of Max D ispl ay is in n umberoftimein terv als rather than secondsIn KR T it is sug
gested to reduce the latency time b y using more memory The problem is that due to high bandwidth
of m ultim edia ob jects to reduce the latency a little a large amoun t of memory is required Ho w ev er w e
use Equation to reduce the latency b y adding more disk c hannels ie increasing R Note that from
Equation the upp er b ound of R is Max D ispl ay ie adding more c hannels will not reduce the latency
time an y further

Figure A sample D A G for Data Driv en P aradigm
Ob ject PlacementF or Data Driv en
The ob ject placemen t for this paradigm is dieren t from that of demand driv en paradigm Ho w ev er the
alternativ e placemen t strategies using replication readahead buering a com bination of replication and
readahead buering and en tirely ash residen t are still applicable
T o illustrate ho w this paradigm migh t b e implemen ted consider the D A G in Figure where p Recall
that with this paradigm one time in terv al is required p er p ossible path Hence time in terv als i i
i are required to displa y all p ossible paths of the D A G in Figure Assuming a six c hannel system that
can supp ort these in terv als the assignmen t of the paths to the in terv als is imp ortan t b ecause it determines
the placemen t of the data and hence the amoun t of resources required Figure demonstrates t w o
p ossible time in terv al assignmen ts for the D AGin Figure T able demonstrates the desired displa y
sc hedule based on time in terv al assignmen t in Figure a
In T able x is displa y ed b y emplo ying one of the six a v ailable in terv als ie i and its displa y is shared
b y all the users This is ac hiev ed bym ultiplexing one stream from a c hannel among the users One migh t
b e tempted to displa y x six times once using eac h time in terv al This w astes resources in t wow a ys First

Figure Impact of time in terv al assignmen t and roundrobin allo cation of in terv als on ob ject placemen t

Reserv ed Time In terv alpath
i xy z u i xz u i xw u i xy u i xz w u i xy z w u
C x
i C y
i C x
C z
i C y
C x
C w
i C x
C z
C z
C u
i C z
C z
C w
C y
C w
C w
T able Placemen t constrain t table for the rst time in terv al assignmen ts
the second time in terv al i is emplo y ed Since the distance bet w een the time in terv als assigned to x i and z i is z
should b e placed on C z
C x
distance C x
In general
C z
j C x
m
q j q
where x
m
is the last sub ob ject of x j and q are the iden tityofthe time in terv als emplo y ed to displa y z and
x resp ectiv ely Using Equation the placemen tof w
can b e computed as follo ws F rom T able iis
assigned to displa y w ie j in Eq imm ediately after the displayof x completes from i ie q
in Eq Hence
C w
C x
C x

Note that C x
can b e computed directly from C x
Generally C x
k
j C x
j k mo d R
A t this p oin t the dierence b et w een C y
and C y
migh t not b e ob vious The reason is that path in y
and hence it is displa y ed b y emplo ying only one time in terv al i Ho w ev er from T able it should b e
ob vious that for example C u
C u
This is b ecause i is emplo y ed to displa y u
after z while iis
emplo y ed to displa y u
after y By applying Equation C o
i can b e determined for eac h ob ject o DAG where i pThe
result can b e summarized in plac ement c onstr aint tables Plac ement c onstr aint tables sp ecify the candidate
c hannels from whic h the placementofeac h ob ject should start F or example T able demonstrates
a plac ement c onstr aint table based on the displaysc hedule in T able As an example lets construct
T able ro wb yro w The rst ro w C x
i is empt y This is alw a ys true for the source of a D A G b ecause
the sour ce has no predecessor Hence there is no constrain t on the placemen t of the source sour ce can
b e placed starting from an arbitrary c hannel T o construct the second row C y
i observ e that since
path in y it is displa y ed only once b y emplo ying i see the rst ro wof T able Therefore C y
for all other in terv als is empt yF or i ho w ev er y
should b e placed imm ediately after x
This is b ecause
the same in terv al whichw as emplo y ed to displa y xis no wemplo y ed to displa y y In other w ords from
Equation C y
C x
C x

By an iden tical discussion
C z
C y

T o compute C z
observ e that although z
should b e displa y ed imm ediately after x
its assigned time
in terv al i is dieren t from that of x i Hence
C z
C x
C x

Similarly other elemen ts of T able can b e computed As the nal example lets compute C u
Since
u
should b e displa y ed from i imm ediately after the displayof y
from i completes then
C u
C y

C y

Reserv ed Time In terv al
F or path
i xzwu x
x
x
x
x
x
z
z
z
z
z
z
w
w
w
w
u
u
u
i xw u w
w
w
w
u
u
u
i xz u u
u
u
i xy z w u y
y
y
y
y
z
z
z
z
z
z
w
w
w

i xy u u
u
u
i xyzu u
u
u
End of path displa y the time in terv al is reserv edbut is idle
F ramed sub ob jects eg u
w
in a column are displa y ed in parallel
T able The displa y of p ossible paths corresp onds to the second time in terv al assignmen t
Reserv ed Time In terv alpath
xz w u xw u xz u xy z w u xy u xy z u
C x
i C y
i C x
C z
i C x
C y
C w
i C z
C x
C z
C u
i C w
C w
C z
C w
C y
C z
T able Placemen t constrain t table for the second time in terv al assignmen t
No w that the constrain t table is constructed placing ob jects to satisfy a data driv en displaysc hedule
similar to T able is trivial F or example the third ro wofT able denotes that the displa yof z
should b e sc heduled from b oth C y
and C x
This can b e ac hiev ed b y sa y replicating z t w o
times An alternativ e is to use readahead buering T o compute the optimal head size of z assume
m
C y
m
C x
No w it is sucien t to compare m
m
with R m
m
applying
Equations and from App endix A and start the placemen tof z from either C
m C
C y or
C
m C
C x Generally for eac h ob ject similar to Section the system can c ho ose to do readahead
buering andor replication as w ell as main taining the en tire ob ject ash residen t
Observ e that if assignmen t of time in terv als is mo died see Figure b and T able then the
placemen t constrain t table w ould c hange as w ell see T able Dieren t placemen t constrain t tables result
in dieren t storage requiremen ts One can generate all the p ossible constrain t tables and c ho ose the one that
results in minim um storage requiremen t lo w er cost Since there are p p ossible time in terv al assignmen ts
the complexit y of this algorithm is O jDAGj p p where jDAGj is the n um b er of ob jects in the D A G
and p is for the maxim um n um b er of constrain ts p er ob ject
Note that this algorithm is applied only once
to place the ob jects The follo wing paragraphs sho w that considering readahead buering is sucien t for
constrain t tables
F or data driv en paradigm the exact amoun t of DRAM requiremen t can b e computed in adv ance The
reason is that all the paths are displa y ed p erio dically Hence it is not required to consider the w orst case
scenarios Th us the price analysis can b e done accurately One heuristic is to rst c ho ose the placemen t
constrain t table whic h results in total minim um DRAM requirement optimal c onstr aint table considering
only readahead buering Next dra wa curv e for DRAM requiremen t for that constrain t table and then
eliminate curv e p eaks b y replication andor storing larger fractions of an ob ject x in ash ie f l ash x H x to reduce the total storage cost This is true b ecause if f l ash x H x d then the system can
p ostp one readahead buering d time in terv als and reduce the n um ber of stable in terv als This migh t also
eliminate the DRAM curv e p eaks
T o b e sp ecic it is O path in o for eac h ob ject o of the D A G p er time in terv al assignmen t

Since the optimal c onstr aint table is determined based on readahead buering the complexit yofthe
algorithm O jDAGj p p can b e reduced further F or example in the last ro wofT able there
are three C w
ie C w
C w
C w
Ho w ev er since readahead buering is emplo y ed there
will b e only one replica of w on disks Subsequen tly there will b e only one ph ysical c hannel con taining w
ie C w
This is indep enden tof path in uwhic h includes three dieren t paths from w Hence from
Section it is sucien t to only consider C w
In other w ords it is sucien t to consider fan in u whic h includes only one edge from w There are some predetermined idle in terv als in T ables and denoted as In addition the exact
lo cation of those in terv als during whichc hannel is not emplo y ed discussed in Section Figure are
no w predictable b eforehand Therefore a sc heduler can assign these idle in terv als for another application
running on the same system
Analysis and Discussion
In this section w e outline the tradeos with the alternativ e paradigms and howtoc ho ose one based on an
applications c haracteristics Next a com bination of b oth paradigms is in tro duced for applications that ha v e
av ariable system load Finally w ein v estigate situations where it is more appropriate to mak e the D A G
en tirely ash residen t
Data Driv en v ersus Demand Driv en
T o decide whic h paradigm to emplo y assume request
is the n um b er of requests referencing the D AGev ery
Max D ispl ay in terv als If the system emplo ys the demand driv en paradigm with R request
c hannels
a new request can nd an empt ytime in terv al most of the time Th us in the w orst case it incurs a
latency time of R time in terv al and at b est no latency un til the emptytime in terv al reac hes the desired
c hannel Hence on the a v erage the latency time observ ed is
request On the other hand if R r eq uest
c hannels are used with the data driv en paradigm from Equation the a v erage latency time w ould b e Max pM ax D isplay p request One can compare the ab o vea v erage latency times and decide whic h paradigm
to c ho ose
An alternativ e is to restrict R and observeho w man y requests can b e supp orted byeac h paradigm with
an iden tical a v erage latency time The paradigm with the highest n um b er of requests can th us b e c hosen
Data Driv en com bined with Demand Driv en
If the n um b er of requests v aries through the life of an application a com bination of b oth paradigms can
b e emplo y ed In this case the system should b e congured for the data driv en paradigm Subsequen tly the system can accum ulate some statistics ab out the n um b er of users referencing the D AGper in terv als
user
If user
p then it executes the data driv en paradigm otherwise it emplo ys the demand driv en
paradigm This is b ecause with data driv en p time in terv als are reserv ed ev ery in terv als Therefore if
there are few er than p users ev ery in terv als it is more ecien t to reserv e time in terv als based on the exact
n um b er of users demand driv en
Once the system decides to switc h paradigms it should abandon the curren t paradigm promptlyT o
observ e assume the system is curren tly using the data driv en paradigm Moreo v er assume that the statistics
suggest that the demand driv en paradigm should b e emplo y ed user
p Once the displa y of one of the
groups of the p ossible paths completes the p a v ailable time in terv als are emplo y ed to service user
requests
that are w aiting for this group one time in terv al p er request Ob viously except the rst user the rest

will observ e a higher latency time as exp ected their displa yw ould ha v e b een started if the system had
con tin ued to use the data driv en paradigm Similarly the displa y of other groups are terminated
During the demand driv en paradigm the system con tin ues accum ulating statistics un til user
p A t
this p oin t once an activ e request is terminated its corresp onding time in terv al is reserv ed Note that
servicing of new requests are stopp ed resulting in higher latencyAs soon as p adjacen t time in terv als are
reserv ed the system starts one group of displa ys of all p ossible paths In a similar manner the displa yof
other groups is started incremen tally as p time in terv als b ecome a v ailable P aradigm switc hing results in
higher latency time observ ed b y the requests arriving during the switc hing p erio d in fa v or of reducing the
latency time observ ed b y the future requests Therefore it migh t not b e wise to switc h paradigm in short
in terv als ev en if the n umberofusers v aries radically T o b e able to com bine the t w o paradigms the D A G should b e placed with resp ect to b oth paradigms A
simple solution is to ha vet w o dieren t copies of the D A G An alternativ e is to place the D A G with resp ect
to b oth paradigms T oac hiev e this it is sucien t to add more columns to the plac ement c onstr aint tables
describ ed in Section b ecause of the demand driv en paradigm These columns add more constrain ts eac h
ob ject should start immediately after the last sub ob ject of its predecessors F or example in the second ro w
of T able y should also start after x
This can b e conrmed b y adding C x
to that ro w Note
that sometimes the new columns do not in tro duce additional constrain ts F or example in the third ro wof
T able new columns are required to conrm that z should start after x
and y
Ho w ev er these t w o
constrain ts ha v e already b een in tro duced for the data driv en paradigm
Comparison with One Lev el Storage Structure
If there are p oten tially large n um b er of users referencing a D A G the question is should the D A G b ecome
en tirely ash residen t Since a large n um b er of users is assumed demand driv en is not appropriate As
compared to the data driv en paradigm if the application cannot tolerate p T ime I nter v al the lo w er
b ound on the maxim um latency time see Equation then the D A G should b ecome ash residen t
In the rest of this section w e assume the maxim um latency tolerated b y an application is higher than
p T ime I nterval One can limit the latency time b y substituting with sa y Max Latency in Equation and compute
R Subsequen tly for this v alue of Rw e can apply the algorithm in Section and compute the total
stor ag e pr ice This price can b e compared with the price of required ash to con tain the en tire D A G
Finally the c heap er one is c hosen of course the exp ected n um ber of sim ultaneous references to the D A G
should also b e considered
Conclusion and F uture Researc h Directions
In this study presen tations sharing clips are represen ted as a D A G The D A G consists of ob jects that
should b e retriev ed at a presp ecied bandwidth in order to supp ort their con tin uous displa y Alternativ e
users migh t displa y dieren t paths of a D A G A path is one p ossible presen tation of information selected
b y the user Tw o alternativ e paradigms demand driv en and data driv en w ere in tro duced The former
is appropriate when the n um b er of resources is greater than or equal to the n um b er of users and the n um b er of p ossible paths is signican tly higher than the amountof a v ailable resources The latter is
appropriate when the demand for data n um b er of users is signican tly higher than the n um b er of resources
Assuming the simple striping placemen t strategyw e demonstrate howeac h paradigm can b e implem en ted
Eac h paradigm in tro duces dieren t placemen t constrain t for the ob jects of a D A G The b est placemen tin
a hierarc h y of storage structure consisting of DRAM ash and disk driv e w as in v estigated based on the
price analysis for eac h paradigm
There are t w o straigh tforw ard extensions to this study First b yc ho osing a D A G to represen t a database

X
Y
Z
X
ZY
X
Y
Z
X
ZY
2-overlap
meet
a. Simple Links b. Information-bearing Links
Figure Straigh tforw ard Extensions
w e restricted ourselv es to me et temp oral relationship as dened in All This is illustrated in Figure a
No w assume eac h link b ears information sp ecifying other t yp es of relationships dened in All F or
example in Figure b displa yofobject X o v erlaps with the displayof Y for t w o sub ob jects or size subobj ect B D isplay
seconds Hence Y should b e placed suc h that its displa y can start imm ediately after X
It is trivial that the tec hniques describ ed in this pap er can supp ort these t yp es of constrain ts with minor
mo dications This is b ecause the problem is the same as b efore except that previously Y should ha v e
b een placed suc h that its displa y can start immedia tely after X
Second in this study w e assumed that
the user c ho ose hisher desired path prior to its displa yHo w everaD A G is placed with no prior kno wledge
ab out the probabilit y that a path mightbe c hosen That is the ob jects of the D A G are placed in order to
pro vide a hiccupfree displa y for all plausible paths Once this is done the system can supp ort an in teractiv e
application as w ell That is a user is not required to c ho ose the complete path b eforehand T o illustrate
consider Figure a The user can b e allo w ed to c ho ose to displa y Y or Z no later than the end of X s
displa y This is b ecause Y and Z are already placed suc h that b oth can b e displa y ed imm ediately after X References
AH D Anderson and G Homsy A cotin uous media IO serv er and its sync hronization IEEE
Computer Octob er All James F Allen Main taining Kno wledge ab out Temp oral In terv als Communic ations of the
A CM No v em b er BGMJ S Berson S Ghandeharizadeh R Mun tz and X Ju Staggered Striping in Multimedia Infor
mation Systems In Pr o c e e dings of the A CM SIGMOD International Confer enc e on Management
of Data
CL HJ Chen and T Little Ph ysical Storage Organizations for TimeDep enden t M ultimedia Data
In Pr o c e e dings of the F oundations of Data Or ganization and A lgorithms F ODO Confer enc e Octob er DH Brian Dip ert and Lou Heb ert Flash memory go es mainstream IEEE Sp e ctrum
F o x E A F o x Adv ances in In teractiv e Digital Multimedia Sytems IEEE Computer pages
Octob er GKS S Ghandeharizadeh S H Kim and C Shahabi Displa yof Con tin uous Media with MultiZone
Magnetic Disks T ec hnical rep ort USC
GKS S Ghandeharizadeh S H Kim and C Shahabi On Conguring a Single Disk Con tin uous
Media Serv er Toapp e ar in Pr o c e e dings of the A CM SIGMETRICS GRA Q S Ghandeharizadeh L Ramos Z Asad and W Qureshi Ob ject Placemen tinP arallel Hy
p ermedia Systems In Pr o c e e dings of the International Confer enceon V ery L ar ge Datab ases Has B Hask ell In ternational standards activities in image data compression In Pr o c e e dings of
Scientic Data Compr ession Workshop pages NASA conference Pub NASA
Oce of Managemen t Scien tic and tec hnical information division
KR T M Kamath K Ramamri tham and D T o wsley Buer Managemen t for Con tin uous Media
Sharing in Multimedia Database Systems In Pr o c e e dings of the International Confer enceon
V ery L ar ge Datab ases PNHV B Prince R Norw o o d J Hartigan and W V ogley Sync hronous dynamic ram IEEE Sp e ctrum R V P Rangan and H Vin Ecien t Storage Tec hniques for Digital Con tin uous Media IEEE
T r ansactions on Know le dge and Data Engine ering August R VR P Rangan H Vin and S Ramanathan Designing an OnDemand Multimeida Service IEEE
Communic ations Magazine July R W A L N Reddy and J C Wyllie IO Issues in a Multimedia System IEEE Computer Magazine Marc h TPBG FA T obagi J P ang R Baird and M Gang Streaming RAIDA Disk Arra y Managemen t
System for Video Files In First A CM Confer enc e on Multime dia August W al S W allace Managing mass storage Byte A On Demand Driv en Complexit y
As describ ed in Section the complexit y of the algorithm to lo cate the b est c hannel to start an ob ject x in
order to minim ize its head size is O path in x R This can b e reduced to O log fan in x fan in x In this section w e describ e this reduction in t w o steps In the rst step w e reduce the complexityto
O log path in x path in x Subsequen tly in the next step w e reduce it further to O log fan in x fan in x Step Consider t w o imp ortan t observ ations from T able Observ ation The rst ro wof T able is iden tical to the c hannel n um b ers con taining the last
sub ob ject of u vand w ie C u
k
C v
l
and C w
m
Observ ation head
i
vertex x head
i v er tex x mo d R This informally means that the v alues in eac h
column is deterministic as a function of the ro ws it is the v alue of the previous rowmin us one except
when the previous v alue is at whic hpoin t it b ecomes R Using the ab o v e observ ations the optimal placemen tof x and the minim um head size H x can b e
determined directly without constructing the en tire table The idea is illustrated in Figure where m
m
m
and m
are the c hannels con taining the last sub ob ject of four dieren t predecessors of an ob ject
x eg if v is a predecessor of x and its last sub ob ject v
l
reside on C
then m
C v
l
Moreo v er
assume they are sorted suc h that m
m
m
m
Figure is a generalized v ersion of T able
Figure F aster metho d to compute minim um head size
The table can b e divided into path in x sections see Figure The rst section includes the
ro ws where m is reduced to Since m is the smallest it reduces to so oner than m
m
and m
Subsequen tly since m
is the largest and in eac h iteration all ms are reduced b y the maxim um of eac h
ro w alw a ys o ccur in m
col umn for the rst section Similarly in the second section m reduces to so oner
The same is true for the third and forth section Since w e are in terested in the maxim um v alue in eachro w
it is sucien t to consider the maxim um column in eac h section Ho w ev er w ew an t to nd the minim um
of these maxim um s The minim um of maxim umsin eac h section ob viously o ccurs in the last rowof that
section F or example in the rst section the maxim um is alw a ys in m
col umn and it is decremen ted in eac h
iteration Hence its minim um v alue o ccurs in the last iteration of that section The v alue of this minim um
of maxim um s for eachv e sections are m
m
R m
m
R m
m
R m
m
and m
resp ectiv ely Moreo v er since m
m
m
H x Min m
m
R m
m
R m
m
R m
m

or in general for n predecessors of x H x Min m
n
m
R m
m
R m
n
m
n

The c hannel n um b er that x should start from is simply iden tical to the rown um b er that the ab o v e minim um
v alue app ears That is
if H x m
n
m
then C x
m

if H x R m
m
! C x
m

if H x R m
n
m
n ! C x
m
n

Therefore once the c hannels con taining the last sub ob ject of path in x predecessors of x is kno wn b y
sorting them in O log path in x path in x and applying Equations and in O path in x w e
can determine the optimal placementof x and H x Hence the total complexit y of this algorithm is
O log path in x path in x

Figure Optimal head size considering fan in y instead of path in y Step T o place y after x see Figure there is no need to consider all three paths ux vxand wx Using the last
observ ation it is sucien t to start the placementof y imm ediately after x indep enden t of the incoming paths
to x Hence the complexit y of the ab o v e algorithm is reduced further to O log fan in x fan in x Ho w ev er note that H y H x and it is not computed from Equation Generally if the algorithm
considers fan in y instead of path in y then Equation will not compute the correct head size T o
observ e assume z as another predecessor to y see Figure and let the last sub ob ject of z sa y z
k
resides
on C
T o place y if the algorithm uses m
C x
and m
C z
k
in Equation it computes
Fan in H y This is not correct b ecause H y needs to b e at least due to paths uxy vxy and wxy Hence
H y Max H x H z F an in H y
Ho w ev er the placemen tof y starts after either x or z dep ends on whether m
m
is smaller or R m
m
from Equation

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Description

Cyrus Shahabi and Shahram Ghandeharizadeh. "Continuous display of presentations sharing clips." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 587 (1994).

Asset Metadata

Creator Ghandeharizadeh, Shahram (author), Shahabi, Cyrus (author)

Core Title USC Computer Science Technical Reports, no. 587 (1994)

Alternative Title Continuous display of presentations sharing clips (title)

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)

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Format 24 pages (extent), technical reports (aat)

Language English

Unique identifier UC16270345

Identifier 94-587 Continuous Display of Presentations Sharing Clips (filename)

Legacy Identifier usc-cstr-94-587

Format 24 pages (extent),technical reports (aat)

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Source 20180426-rozan-cstechreports-shoaf (batch), Computer Science Technical Report Archive (collection), University of Southern California. Department of Computer Science. Technical Reports (series)

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Repository Name USC Viterbi School of Engineering Department of Computer Science

Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089

Repository Email csdept@usc.edu

Inherited Values

Title Computer Science Technical Report Archive

Coverage Temporal 1991/2017

Repository Email csdept@usc.edu

Repository Name USC Viterbi School of Engineering Department of Computer Science

Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)