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USC Computer Science Technical Reports, no. 602 (1995)

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USC Computer Science Technical Reports, no. 602 (1995)

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Content An Optimal Resource Sc heduler for Con tin uous
Displa y of Structured Video Ob jects
Martha L EscobarMolano Shahram Ghandeharizadeh
Douglas Ierardi
fmarthae shahram ierardi gp olluxuscedu
July Abstract
This study presen ts an optimal resource sc heduler for con tin uous displa y of structured video
A structured video consists of a collection of bac kground ob jects c haracters and rendering
features Spatial constructs are used to place ob jects that constitute a scene in a rendering
space while temp oral constructs describ e ho w the ob jects and their relationships ev olveas a
function of time When a user requests the displa y of a video ob ject the system is pro vided
with a displaysc hedule of ob jects that m ust b e retriev ed b y a certain time in order to supp ort
a displa y free of disruptions Assuming a platform consisting of a xed amoun t of memory and
a magnetic disk driv e this study describ es an algorithm that supp orts suc h a retriev al while
minim i zing b oth the latency observ ed b y a displa y and its required amoun t of memory Keyw ords Multimedia Databases Optimization Resource Sc heduling Con tin uous Dis
pla y Structured Video
This researchw as supp orted in part b y the National Science F oundation under gran ts IRI IRI
NYI a w ard and CD A and a HewlettP ac k ard unrestricted cashequipmen t gift
In tro duction
An emerging area of database researchis toin v estigate tec hniques that ensure a con tin uous dis
pla y of video ob jects Rep ositories supp orting this data t yp e are exp ected to pla y a ma jor role
in man y applications includin g library information systems en tertainmen t industry educational
applications etc A rep ository ma y employt w o alternativ e approac hes to represen t a video clip
Streambased A video clip consists of a sequence of t w o dimensional frames Its frames are
displa y ed at a presp ecied rate eg frames a second for TV sho ws frames a second
for most mo vies sho wn in a theater due to the dim ligh ting If an ob ject is displa y ed at a
rate lo w er than its presp ecied bandwidth its displa y will suer from frequen t disruptions
and dela ys termed hic cups Structured A video clip consists of a sequence of scenes Eac h scene consists of a collection
of bac kground ob jects actors eg dimensional represen tation of Mic k ey Mouse dinosaurs
lions ligh t sources that dene shading and the audiences view p oin t Spatial constructs are
used to place ob jects that constitute a scene in a rendering space while temp oral constructs
describ e ho w the ob jects and their relationships ev olv e as a function of time The rendering
of a structured presen tation is hiccupfree when it satises the temp oral constrain ts imp osed
on the displayof eac h ob ject Reb o ot Ber is an animated Saturda y morning c hildrens
sho w created using this approac h The adv an tages of using this approac h is that its con ten t
description captured in the structure can facilitate eectiv e query pro cessing tec hniques
Moreo v er it supp orts reusabilit y of information b ecause an ob ject can b e extracted from
one scene and reused in another
The fo cus of this study is on structured video ob jects Our target hardw are platform consists
of a xed amoun t of memory DRAM and a mass storage device a magnetic disk driv e The size

T erm Denition
t Duration of a time in terv al
m Duration of a mo vie in time in terv als
T
p
Time to retriev e a page
Time In terv al i P erio d i i Instan t i The b eginning of time in terv al i
p
max
Maxim um n um b er of pages read during a time in terv al
S
i
P ages in memory at instan t i
RS
i
P ages that m ust b e in memory at instan t i
P
i
P ages con taining ob jects displa y ed during time in terv al i
F
i
P ages retriev ed from disk on to memory during time in terv al i
R
i
P ages sw app ed out during time in terv al i
T able P arameter Denitions
of memory is signican tly smaller than that of the magnetic disk driv e All ob jects along with
their complex relationships reside on the magnetic disk driv e p ermanen tly When a user requests
the displa y of a video clip the system is pro vided with a display sche dule The displa ysc hedule
sp ecies when eac h participating ob ject should b e memory residen t in order to supp ort a hiccup
free displa y The ob jects are staged from disk in to memory prior to their displa y Ho w ev er if
an ob ject is already memory residen t then the system observ es a memory hit and do es not access
the disk driv e This study presen ts an optimal resource sc heduler that emplo ys the information
pro vided b y the displaysc hedule to construct a r etrieval sche dule for staging ob jects from the
disk driveon to memory It pro vides for a hiccupfree displa y while minimizing the follo wing t w o
criteria the latency observ ed b y a displa y ie time elapsed from the arriv al of a request to the
onset of the displa y and the amoun t of memory required for the displa y These t w o goals are
complemen tary and in this case the algorithm minimizes b oth sim ultaneously
Mo del
When a user requests the displa y of a structured video the system has adv anced kno wledge of
the iden tit y of ob jects that should b e memory residen t at sp ecic times to supp ort a hiccupfree
displa yT o render the retriev al sc hedule from the disk driv e regular w e partition time in to units
of xed size termed time intervals of duration t Let m b e the duration of the mo vie in time
in terv als Assume that a disk page is the unit of transfer b et w een the disk driv e and memory Without loss of generalit yw e assume that the size of an ob ject is smaller than the size of a disk
page When an ob ject violates this assumption w e represen t it as a sequence of xsized pages
The assignmen t of the ob jects to the pages is predetermined
and the displa y of an ob ject do es
not mo dify this assignmen t If the time required to read a page is denoted as T
p
the system can
read a maxim um of p
max
b
t
T p
c pages during a time in terv al Ob jects displa y ed during time
in terv al i m ust b e memory residen t during the en tire in terv al i for i from to m Let P
i
denote the set of pages con taining these ob jects With these constrain ts a displa y assigns a set of
pages that m ust b e memory residen t at the b eginning of time in terv al i termed residen t set RS
i

to ensure a hiccupfree displa y Henceforth the b eginning of a time in terv al i is termed instan t
i RS
i
includes pages con taining ob jects displa y ed during time in terv al i and those con taining
ob jects to b e displa y ed during in terv al i ie RS
i
P
i
P
i for i m RS
P
RS
m
P
m Wein terlea v e the displa y and the retriev al of disk pages to reduce b oth the latency time
observ ed b y a displa y and its memory requiremen ts
Ideally P
i
should b e retriev ed in to memory
during time in terv al i as this minimizes the amoun t of required memoryHo w ev er this is not
alw a ys p ossible b ecause the n um b er of pages that constitute P
i
ma y exceed p
max
In this case the
The placemen t of ob jects across the pages do es not constitute the fo cus of this study It is an imp ortan t researc h
topic that deserv es further in v estigation An alternativ e is to retriev e all disk pages from memory b efore initiating the displa yHo w ev er this approac h
requires a signican tamoun t of memory Moreo veritdela ys the displayun til all ob jects b ecome memory residen t

a Example Time table of displa y b Example Optimal retriev al sc hedule
Figure In b arro ws iden tify the retriev al of a page from the disk driv e while b o xes indicate
ho w long the page remains memory residen t
retriev al of some pages of P
i
are pushed to earlier time in terv als i i etc These pages
are termed pr efetche d pages Note that prefetc hed pages increase the memory requiremen t of the
system and their coun t should b e minimized Let S
i
denote the set of pages in memory at instan t
i Therefore in addition to RS
i
S
i
ma y con tain prefetc hed pages for in terv als i i etc The displa y of an ob ject do es not start un til S
b ecomes memory residen t The size of S
determines the elapsed time from the arriv al of a request to the onset of its displa y the latency
observ ed b y a user By minimizing the n um b er of pages in S
denoted jS
j the system minimizes
this latency time
A valid r etrieval sche dule is a sequence S
S
m
suc h that the follo wing t w o ob jectiv es
are satised First it m ust satisfy the temp oral constrain ts to ensure a hiccupfree displa y ie
RS
i
S
i
Second the n um b er of pages that constitute S
i
S
i
should b e smaller than or equal to
p
max
for all i i m Otherwise it violates bandwidth restriction A v alid retriev al sc hedule
is optimal if the n um b er of disk pages that constitute S
i
is minimized for ev ery time in terv al i i m This minimizes b oth the memory requiremen t of the system and the latency observ ed
b y a user
Example Consider a request to displa y a structured video consisting of time in terv als with

ob jects displa y ed at eac h time in terv al residing in the follo wing disk pages
P
fa b c g P
fa d g P
fa e g P
fa c f g
P
fa b g P
fa e g P
fa f g g P
fag
Figure a illustrates the time table of the displa y The pages in S
are retriev ed during the p erio d
bet w een the arriv al of the request and the b eginning of the displa y The state of memory at the
b eginning of eac h time in terv al S
i
m ust con tain the pages in the residentsets RS
i
to ensure a
hiccupfree displa y
RS
fa b c g RS
fa b c d g RS
fa d e g RS
fa c e f g RS
fa b c f g
RS
fa b e g RS
fa e f g g RS
fa f g g RS
fag
Of the quan tities describ ed ab o v e b oth P
i
and RS
i
are determined b y the structured ob ject
The system derivesav alid retriev al sc hedule based on the a v ailable bandwidth of its disk driv e
to ensure a hiccupfree displa yF rom a v alid retriev al sc hedule w e can deriv e the pages retriev ed
from disk to memory F
i
and the pages discarded from memory R
i
for eac h time in terv al i These quan tities are dened as follo ws
F
i
S
i
S
i
and R
i
S
i
S
i If S
i
exceeds the size
of a v ailable memory for a time in terv al then there is insucien t memory to supp ort a con tin uous
displa y This scenario do es not constitute the fo cus of this study A straigh tforw ard solution migh t
b e to increase the amountof a v ailable memory F or the rest of this pap er w e describ e an optimal
algorithm that realizes these three ob jectiv es
Ob viouslyan y other sequences fF i g and fR i g pro viding the same retriev al sc hedule m ust p erform redundan t
w ork eg retrieving a page that is already memory residen t

Optimal Resource Sc heduler
F or eac h time in terv al i and page aw e dene last a i to b e the most recen t instan t j j iat
whichpage a w as referenced More formally let last a and for eac h i dene
last a i i if a P
i last a i otherwise
The goal of the resource sc heduler is to minimize b oth the latency and the total amoun t
of memory required to supp ort con tin uous displa y The greedy sc heduler tak es as input a re
quest hP
P
m ip
max
and pro duces a complete retriev al sc hedule that sp ecies the sequence
S
S
m
Greedy Sc heduler hP
P
m ip
max
S
m
RS
m
for i m to do
Let D
i
b e the sequence of pages in S
i RS
i
sorted b y last i if jD
i
j p
max
then F
i
D
i
else F
i
fthe rst p
max
pages in D
i
g
S
i
RS
i
D
i
F
i
end for
The latency is djS
jp
max
e time in terv als The memory requiremen t of the retriev al sc hedule
is max
i m
jS
i
j The request is rejected if this quan tit y exceeds C the maxim um n um ber of
memory pages a v ailable W e demonstrate the sc heduler using an example Subsequen tlyw e pro v e
its optimalit y Example Figure b illustrates the retriev al sc hedule computed b y the algorithm for the

video ob ject in Example when p
max
The memory required to displa y the video is page
frames ie max
i jS
i
j And the latency is time in terv als
Consider the lo op iteration when i ie the sc hedule of retriev als for time in terv al The
state of the v ariables is as follo ws S
fa e f g g RS
fa b e g D
ff g g The system
can only retriev e either f or g but not b oth b ecause p
max
The sc heduler retriev ed g b ecause
f m ust b e retriev ed prior to time in terv al f P
while g P
j
for j In other w ords
l ast g l ast f Therefore f remains memory residen t during three time in terv als
from in terv al to If the sc heduler retriev es f instead of g then the system m ust allo cate some
bandwidth to retriev e g at an earlier time in terv al There are t w o alternativ e approac hes First
increase the latency and retriev e g prior to time in terv al Second retriev e g instead of b e during
time in terv al and render b e memory residen t from time in terv al to to The rst
alternativ e increases latency to time in terv als while the second increases the memory requiremen t
to page frames b ecause S
S
no w consists of fa b c d e g fa b c e f g Theorem The retriev al sc hedule pro duced b y the greedy sc heduler is optimal
Pro of Consider a request Rq hP
P
m ip
max
Let G S
g
S
g
m
denote the retriev al
sc hedule pro duced b y the greedy sc heduler on Rq It suces to pro v e that for anyv alid retriev al
sc hedule S S
S
m
for Rq jS
g
i
jj S
i
j for all i m T o pro v e this w e transform S
in to G state b y state starting with S
m
and ending with S
Sp ecically w esho w inductiv ely that
for eac h i there is a w a y of transforming states S
S
m
in to a sequence of states S
S
m
so that these transformations do not require extra memory nor do they ev er exceed the a v ailable
bandwidth More formally for all j m jS
j
j j S
j
j and for all j i S
j
S
g
j
It will
follo w that the memory requirementof G at eac h instan t is optimal Therefore the total memory
requirementmax
i m
jS
g
i
j is minimized Moreo v er the latency is also minimized b ecause it is

determined b y jS
g
j F or the basis of the induction consider S
m
then either S
m
S
g
m
RS
m
or S
g
m
S
m
W e
can eliminate all pages in S
m
S
g
m
ie S
m
S
g
m
b ecause they are not displa y ed during time
in terv al m F or the induction step supp ose that w eha v e transformed S so that S
j
S
g
j
for all
j i m T o simplify notation from no won w e denote transformed sequences b y S instead
of S
Consider the p ossible dierences b et w een S
i
and S
g
i
If S
i
S
g
i
then there is nothing to
do
Supp ose that S
i
S
g
i
Hence there are pages a S
i
S
g
i
that S has residen t and G
do es not Since a S
g
i
then a RS
i
So these sets can b e equated byremo ving a from S
i
and propagating this c hange bac kw ards There are sev eral cases needed to realize this bac kw ards
propagation If a S
i then eliminate it from S
i
If a S
i S
g
i then a can b e retriev ed
during time in terv al i in S as long as there is sucien t bandwidth a v ailable to accommo date this
retriev al In this case a is eliminated from S
i
Assume that there is insucien t bandwidth to
supp ort the retriev al of aHence S is retrieving p
max
pages during iIt follo ws that G retriev es a
during i b ecause a S
g
i
and a S
g
i
Moreo v er it m ust b e the case that there is some other page
b a that is retriev ed b y S during i but not retriev ed b y G Because G retriev es at most p
max
pages during ev ery time in terv al Ho w ev er b y the inductiveh yp othesis S
i S
g
i so b S
g
i
th us b RS
i
Therefore last a i last b i T oequate S
i
and S
g
i
S will no w exc hange the
in terv als during whic h a and b w ere retriev ed There are t w o cases First if a is retriev ed after
last b i then let j to b e the in terv al when a w as retriev ed In this case one sw aps the retriev al of
a with that of b so that
for k j i S
k
S
k
f ag f bg If b w as already presen t in memory when a w as retriev ed in S then no retriev al is actually needed

the mo dications main tain b memory residentun til in terv al i Second if a is retriev ed previous
to or at last b i then w eset j last b i Since b is in S
j
main tain b in memory un til i as in
Equation These transformations increase neither the memory nor the bandwidth requiremen t
ofain terv al
Symmetricallyit ma y b e the case that S
g
i
S
i
Th us G has made some page b memory
residen t that is not residentin S at iHo w ev er since S is a v alid retriev al sc hedule it m ust b e
the case that eac h suc h b is not in RS
i
This implies that b S
g
i S
i as w ell and G retriev ed
p
max
pages during iTh us there m ust b e some page a that G retriev es during i that S do es not
retriev e The nature of the greedy algorithm implies that last a i last b i But b y the inductiv e
h yp othesis S has a S
i Since S do es not retriev e a during time iitm ust ha v e a S
i
T o
equate S
i
and S
g
i
mo dify S so that a is retriev ed instead of b during i and propagate the c hange
through previous in terv als as ab o v e
Note that there are transformations for eac h p ossible dierence b et w een S
i
and S
g
i
Therefore
the greedy algorithm pro duces an optimal retriev al sc hedule
Since the greedy sc hedule minimizes the memory requirementat eachin terv al it m ust b e the
case that whenev er it is p ossible to sc hedule the request using memory Csuc hasc hedule will b e
found It is not dicult to see that an optimal retriev al sc hedule can b e computed in time O n lg n where n
m i
jP
i
j Discussion
This pap er describ es an optimal resource sc heduler that ensures a hiccupfree displa y of structured
video while minimizing b oth the latency incurred b y a displa y and its total memory requiremen ts
One resource managed b y our sc heduler is memory The previous studies of cac hing attempt

to minimize the n um b er of misses scored b y references to pages that are not residen t in a x
sized cac he P age replacemen t algorithms based on heuristics eg LR U MR U LR UK OO W and FIF O are widely used in applications where future page references are unkno wn Optimal
strategies ha v e b een presen ted for the case where the en tire sc hedule of page references is kno wn
CR and comp etitiv e online algorithms ha v e b een studied for online v arian ts of this problem
in whic h an unkno wn sequence of references is generated byan adv ersary ST or b ya Mark o v
pro cess In addition these results ha v e b een generalized and elab orated to deal with data placemen t
in distributed systems and le migration MS
Ho w ev er neither heuristic based nor optimal strategies ha v e considered temp oral constrain ts
suc h as the one that supp orts a hiccupfree displa y The resource sc heduler describ ed in this study
do es not aim to minimize the n um b er of page faults Instead it striv es to assure a hiccupfree
displa y while minimizing the latency observ ed b y the user By minimizing the memory requiremen t
of the system it minimizes the observ ed latency Sev eral studies ha vein v estigated the retriev al of streambased presen tations CL NY DP A G Ho w ev er they do not consider data sharing in memory Kamath et al MKT in tro duced a data cac hing metho d that preserv es buers in a con trolled fashion for use b y other
activ e displa ys This tec hnique striv es to reduce the total n um b er of disk IOs b y maximizing
memory hits Con v ersely our sc heduler striv es to utilize all a v ailable disk bandwidth to minimize
b oth the latency and the amoun t of memory required for a single displa y of structured video
An um b er of studies ha v e analyzed tec hniques to sc hedule tasks with realtime deadlines HL CRS RS These studies sc hedule the CPU with the ob jectiv e to minimize the total cost to
the system the n um b er of tasks that miss their realtime deadline and their asso ciated cost This
study is no v el b ecause w e fo cus on IO sc heduling and cac hing that are k ey pro cessing comp onen ts

of a data in tensiv e application There are no deadlines on when a displa y should start Instead
once a displa y is started the computed retriev al sc hedule supp orts the displaysc hedule to pro vide
for a hiccupfree displa y Wein tend to extend this study in sev eral w a ys First w e plan to in v estigate the role of
m ultiple disk driv es and ho w their aggregate bandwidth can b e used to minimize b oth the memory
requiremen t and latency time of the system In this en vironmen t the placemen t of data across
the disks is of paramoun t imp ortance Second the prop osed algorithm should b e extended for
an en vironmen t consisting of m ultiple users displa ying structured video Dieren t presen tations
ma y share individual ob jects In this case w e plan to in v estigate howm ultiple sc hedules eac h
sc hedule corresp onding to one activ e displa y can b e co ordinated to minimize the a v erage latency Finallyw ein tend to extend the algorithm to supp ort dynamic presen tations of structured displa ys
With a dynamic presen tation the user con trols the displayin teractiv ely An example is a virtual
represen tation of geographical data with a na vigator con trolling the displa y Ensuring a con tin uous
displa y migh t require reserv ation of resources b oth disk bandwidth and memory
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Description

Martha L. Escobar-Molano, Shahram Ghandeharizadeh and Douglas Ierardi. "An optimal resource scheduler for continuous display of structured video objects." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 602 (1995).

Asset Metadata

Creator Escobar-Molano, Martha L. (author), Ghandeharizadeh, Shahram (author), Ierardi, Douglas (author)

Core Title USC Computer Science Technical Reports, no. 602 (1995)

Alternative Title An optimal resource scheduler for continuous display of structured video objects (title)

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

Tag OAI-PMH Harvest

Format 13 pages (extent), technical reports (aat)

Language English

Unique identifier UC16269494

Identifier 95-602 An Optimal Resource Scheduler for Continuous Display of Structured Video Objects (filename)

Legacy Identifier usc-cstr-95-602

Format 13 pages (extent),technical reports (aat)

Rights Department of Computer Science (University of Southern California) and the author(s).

Internet Media Type application/pdf

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

Access Conditions The author(s) retain rights to their work according to U.S. copyright law. Electronic access is being provided by the USC Libraries, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

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

Description Archive of computer science technical reports published by the USC Department of Computer Science from 1991 - 2017.

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)