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USC Computer Science Technical Reports, no. 909 (2009)

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USC Computer Science Technical Reports, no. 909 (2009)

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Content An Enhanced Safe Region Technique for
Continuous Queries over Moving Objects
Yu-Ling Hsueh
y
Roger Zimmermann
z
Wei-Shinn Ku
x
y
Dept. of Computer Science, University of Southern California, USA
z
Computer Science Department, National University of Singapore, Singapore
x
Dept. of Computer Science and Software Engineering, Auburn University, USA
fhsueh@usc.edu, rogerz@comp.nus.edu.sg, weishinn@auburn.edug
Abstract. Continuous spatial queries retrieve a set of time-varying ob-
jects continuously during a given period of time. However, monitoring
moving objects to maintain the correctness of the query results often
incurs frequent location updates from these moving objects. To address
this problem, existing solutions propose lazy updates, but such tech-
niques generally avoid only a small fraction of all unnecessary location
updates because of their basic approach (e.g., safe regions, time or dis-
tance thresholds). Furthermore, most prior work focuses on a simpli¯ed
scenario where queries are either static or rarely change their positions.
In this paper, we introduce an Adaptive Safe Region (ASR) technique
that retrieves an adjustable safe region which is continuously reconciled
with the surrounding dynamic queries. The communication overhead is
reduced in a highly dynamic environment where both queries and data
objectschangetheirpositionsfrequently.Inaddition,wedesignaframe-
workthatsupportsmultiplequerytypes(e.g.,rangeandc-kNNqueries).
In this framework, our query re-evaluation algorithms take advantage of
ASRs and issue location probes only to the a®ected data objects, with-
out°oodingthesystemwithmanyunnecessarylocationupdaterequests.
Simulationresultscon¯rmthattheASRconceptimprovesscalabilityand
e±ciency over existing methods by reducing the number of updates.
1 Introduction
Signi¯cantresearchattentionhasfocusedone±cientlyprocessingcontin-
uous queries and its extension work that supports location-based services
during the recent past. The advancement of mobile technologies such as
IEEE 802.11x networks, cellular communications and GPS sensors en-
ables a server to track the positions of moving objects and provide var-
ious location-based services. Many existing techniques [5{7,10,11] have
proposed continuous monitoring approaches without considering the cost
of the communication overhead involved. Some prior work [4,8,9] has
provided signi¯cant insight into these issues by assuming a set of com-
putationally capable moving objects that cache query-aware information
(e.g., thresholds or safe regions) and locally determine a mobile-initiated
location update. However, the focus of these solutions is mainly on static
queries or simple types of queries (e.g., range queries). If query move-
ments are frequent, such systems su®er from repeated location detections
to resolve location ambiguity (incurred on the objects that might be-
come result points) and numerous down-link messages sent to refresh the
query-aware information on those mobile objects.
In this paper, we propose a framework to support multiple types of
dynamic, continuous queries. Our goal is to minimize the communication
overheadinahighlydynamicenvironmentwherebothqueriesandobjects
change their locations frequently. When a new query enters the system
we leverage the trajectory information that it can provide by registering
its starting and destination points as a movement segment for continu-
ous monitoring. For example, a policeman might request the following
a mobile-initiated
update
a server-initiated
update
ASR
2
p
1
p
1
q
3
p
Range
MR
8
p
8
p c ASR
actual query
region
2
q
6
p
5
p
7
p
c-3NN
9
p
4
p
10
p
2
q c (a) An example of ASRs.
5
p
2
q
6
p
10
p
7
p
9
p
4
p
traditional expanded query
region
2
q c (b) A query expansion.
Fig.1. System overview.
query: \send me the closest 5 police cars on the road as I am moving
from point A to point B." For simplicity, we assume a straight movement
segment between two points. This assumption can be easily extended to
a more realistic scenario which may approximate a curved road segment
with several straight-line sub-segments. We propose an adaptive safe re-
gion that reconciles the surrounding queries based on their movement
trajectories such that the system can avoid unnecessary location probes
totheobjectsinthevicinity(i.e.,theoneswhichoverlapwiththecurrent
query region). The basic concept of a safe region is that a moving object
that stays within the given safe region does not a®ect any query results.
Therefore,alocationupdateisnecessaryonlywhenamovingobjectexits
its safe region. Furthermore, our incremental result update mechanisms
allow a query to issue location probes only to a minimum area where the
query answers are guaranteed to be ful¯lled. In particular, to lower the
amortizedcommunicationcostforc-kNNqueries,weobtainextranearest
neighbors (n more NNs) which are cached and reused later to update the
query results. Thus, the number of location updates incurred from the
query region expansion due to query movement is reduced. An example
isshowninFigure1(a).TheASR ofp
3
isdeterminedbasedontheclosest
query q
1
, since p
3
has a high probability of being covered by the query
regionofq
1
whenq
1
movesinthefuture.Thesaferegionof p
3
isadjusted
to an appropriate size according to the trajectory information of q
1
. The
saferegionforp
8
issimplysettothemaximumnon-overlappingareawith
the query region of q
2
, because q
2
(due to its opposing movement direc-
tion) will never cover p
8
. We bu®er one extra NN for q
2
(a c-3NN query).
When q
2
moves to q
0
2
, and since the number of NNs is equal to 3, the
query region remains unchanged. In the traditional approach (as shown
in Figure 1 (b)), the query region is expanded to cover p
5
(the ¯rst clos-
est object outside the query region) such that additional location probes
to p
7
, p
9
, and p
10
are issued. Overall, our approach reduces the number
of query expansions to ¯nd su±cient NNs and the number of location
probes. In summary, the contributions of this paper are as follows:
1. We propose a framework that supports multiple types of dynamic
queries over moving objects and minimizes the communication over-
head in a highly dynamic environments.
2. The concept of adaptive safe regions is introduced to enhance tradi-
tionalsaferegions.Thenumerousdownlinklocationprobesasaresult
of frequent query movements are reduced.
3. Our approach sends downlink ASR transmissions to a small set of
objects a®ected by a query movement or an insertion of a new query.
4. Weproposeenhancedincrementalqueryupdatealgorithmsthatresult
in fewer location probes (e.g., through extra n NNs).
Data
Set
Data
Points
Query
Points
Request
NNs Order
Checks
Boundary
Expansion
I/O Access
Request
Location Probes
Location Probes
Query Results
Query Processor
Result
Monitoring
B
A
F
G
H
ASR
Computation
ASR Assignments
I
Range Query
Evaluation
C-kNN Query
Evaluation
Result
Set
C
D
E
Fig.2. System architecture overview.
Figure 2 shows the system framework. When a request arrives from a
data point (A) or from a query point (B) (e.g., a location update, query
insertion or deletion), the ASR query processor checks whether the point
is part of a query result in modules (C) and (D). To incrementally up-
date a query result, prior query results (E) are considered. For a c-kNN
query, an NN order check (F) is performed during the query evaluation
process. While there are less than k NNs in the result set, a query region
expansion (G) is executed. Some server-initiated location probes might
be needed to resolve location ambiguities. The points in the result set are
monitored (H) through a passive mechanism { this result set is di®erent
from the non-result points that voluntarily issue location updates locally
determined by the objects. Finally, an updated data point is assigned
a new ASR based on the current query information in module (I). De-
tailed descriptions of the functionalityof each component will be given in
Section 3. The remainder of this paper is organized as follows. Section 2
describes the related work. Section 3 presents the adaptive safe region
computations and continuous query update mechanisms. We extensively
verifytheperformanceofourtechniquesinSection4and¯nallyconclude
the paper in Section 5.
2 Related Work
Continuous monitoring of queries over moving objects has become an
important research topic, because it supports various useful mobile ap-
plications. Prabhakar et al. [9] designed two approaches named query
indexing and velocity constrained indexing with the concept of safe re-
gions to reduce the number of updates. The MQM solution [1] leverages
the computational capabilities of moving objects for e±cient processing
of continuous range queries. Hu et al. [4] proposed a generic framework
tohandlecontinuousquerieswithsaferegionsthroughwhichthelocation
updates from mobile clients are further reduced. However, these methods
only address part of the mobility challenge since they are based on the
assumption that queries are static which is not always true in real world
applications.
By employing grid indices, a number of methods (e.g., LUGrid [12])
have been proposed to process dynamic continuous queries over moving
objects. MobiEyes [3] presented a distributed infrastructure to process
dynamic range queries where the server is acting as a mediator to coor-
dinate query processing on both the server and moving objects. Mokbel
et al. proposed the SINA algorithm [6] for evaluating a set of concur-
rentcontinuousspatio-temporalqueries.Withtheincrementalevaluation
paradigm,SINAupdatesqueryresultsbycomputingandsendingonlyin-
crements of the previously reported answer. Yu et al. [13] proposed an
approach that continuously monitors a kNN query by de¯ning a search
region based on the maximum distance between the query point and the
locations of current kNN query results. Moving object data are assumed
to ¯t in main memory and are indexed with a regular grid. However, the
algorithm su®ers from high re-evaluation cost when the query point is
highly mobile. The SEA-CNN framework designed by Xiong et al. [11]
is based on the concepts of incremental evaluation and shared execution.
Movingobjectsarestoredinsecondarymemoryandindexedwitharegu-
largrid.SEA-CNNcontinuouslymaintainsthe search radius ofthequery
pointtoavoidrecomputingthequeryresultsoncethequerypointchanges
its location. The conceptual partitioning (CPM) [7] method assumes the
same system architecture and indexing structures as SEA-CNN. CPM
de¯nesaconceptualpartitioningofthespacebyorganizinggridcellsinto
larger rectangles. Location updates are handled only when objects move
into the vicinity of queries and hence system throughput is improved. A
threshold-based algorithm is presented in [8] which assumes that moving
objects have some computational capabilities and aims to minimize the
network cost when handling c-kNN queries. A threshold is transmitted
to each moving object and when its moving distance exceeds the thresh-
old,themovingobjectissuesanupdate.However,thesystemsu®ersfrom
manydownlinkmessagetransmissionsforrefreshingthethresholdsofthe
entiremovingobjectpopulationduetofrequentquerymovements.Cheng
et al. [2] proposed a time-based location update mechanism to improve
the temporal data consistency for the objects relevant to queries. Data
objects with signi¯cance to the correctness of query results are required
to send location updates more frequently. The main drawback of this
method is that an object will repeatedly send location updates to the
server when it is enclosed by a query region.
Incontrast,ourproposedtechniquesaimtoreducethecommunication
cost of dynamic queries over moving objects and also support multiple
types of queries. We utilize adaptive safe regions to reduce the down-
link messages of location probes due to query movements. To further
reduce the downlink messages, our incremental query update approach
only probes a set of objects that might become part of the query results.
Additionally,ourapproachallowsfordecoupled,query-awareinformation
tobelocallymaintainedbyeachmovingobjectuntilthemovementmight
a®ectthequeryresults.OurASR-basedtechniquessurpasstheaforemen-
tioned solutions with higher scalability and lower communication cost.
3 System Overview
The mobile units are partitioned into a set of dynamic query objects Q
and a set of moving objects P. Each query object registers its movement
trajectory with the server by uploading its starting and ending points
(denoted by
¡ !
q
j
= [q
s
j
;q
e
j
]). Furthermore, all the data objects can move in
a non-restricted fashion that allows them to move arbitrarily. We assume
a maximum speed ± for both query and data objects. The server uses a
main-memory grid G consisting of w£w cells of uniform length for each
dimension to index the moving objects. The query processor evaluates
the queries based on the query types in an event-triggered manner. The
locations of all queries are monitored by the server.
The location updates of a query result point (result point for short)
and a non-result point (data point for short) are handled with two dif-
ferent mechanisms. An adaptive safe region (ASR) is computed for each
data point. A mobile-initiated voluntary location update is issued when
any data point moves out of its safe region. An example (p
8
) is shown
in Figure 1 (a). To capture the possible movement of a result point, we
use a moving region (MR) whose boundary increases by the maximum
movingdistancepertimeunit.Fortheresultpoints,thelocationupdates
are requested only when the server sends server-initiated location probes
triggered when the moving regions of the result points overlap with some
query regions. The details of the adaptive safe region computation are
described in Section 3.1. We present an e±cient continuous query update
approach and propose a mechanism that uses location probes to solve
location ambiguity in Section 3.2. Table 1 summarizes the symbols and
functions we use throughout the following sections.
Symbol Description
Q A set of query objects
P A set of moving objects
G A w£w object grid where objects are hashed to the grid cells based
on their locations
± Maximum speed for any object
pi:ASR Adpative safe region of object pi
p
i
:MR Moving region of object p
i
q
j
:QR Query region of query q
j
(the radius is denoted by q
j
:QR:radius)
¡ !
qj Movement trajectory of qj
q
s
j
Staring point of the movement trajectory for q
j
q
e
j
Ending point of the movement trajectory for qj
Table 1. Symbols used in this paper.
3.1 Adaptive Safe Region Computation
The existing work adopts safe regions to reduce unnecessary location
updatessuchthatthecommunicationcostbetweentheserverandmoving
objects is reduced. A safe region in a traditional system is simply an area
of maximal size around an object such that no query regions overlap.
Figure3(a)showsanexampleoftwosuchsaferegiontypes(asafesphere
and a safe rectangle) for object p
1
. However, this approach su®ers from
many location updates as a result of frequent query movements. When a
querymoves,theserverinitiateslocationprobestothedataobjectswhose
saferegionsoverlapwiththequeryregiontoensurethecorrectnessofthe
query answers. In this paper, we propose a novel approach to retrieve an
adaptive safe region (ASR), which is often smaller than a maximum non-
overlapping region and yet is very e®ective in reducing the amortized
communication cost in a highly dynamic mobile environment. The key
observation lies in the consideration of some important factors (e.g., the
velocityororientationofthequeryobjects)toreconcilethesizeofthesafe
regions. Figure 3 (b) illustrates the concept of an ASR. The on-demand
x
1
p
2
q
y
c-kNN
range
3
q
range
1
q
z
safe sphere
safe rectangle
(a) A traditional safe region.
x
2
q
y
range
3
q
range
z
2
r
2
r
y
z
3
r
3
r
adaptive safe region
c-kNN
1
q
1
r
1
r
x
1
p
(b) An adaptive safe region.
Fig.3. Traditional safe region v.s. adaptive safe region.
location probes are issued as soon as any surrounding queries (q
1
, q
2
, or
q
3
)move.Inthisexample,thedistancez istheASR radiusofp
1
,because
in the worst case, after both q
3
and p
1
move by distance z and p
1
moves
directly toward q
3
, p
1
may become a result point of q
3
. The following
lemma establishes the ASR radius based on this observation.
Lemma 1:
p
i
:ASR:radius=min(CDist(p
i
;q
j
)¡q
j
:QR:radius);8q
j
2Q, where
CDist(p
i
;q
j
)=
8
>
<
>
:
p
i
f
0
if µ
j
·
¼
2
and9f
0
, or
p
i
q
s
j
if µ
j
>
¼
2
or@f
0
As an illustration of Lemma 1 (and to explain the symbol notation),
consider Figure 4, where the set of queries Q = fq
j
;q
k
g are visited for
retrieving the adaptive safe region (the dashed circle) of the data point
p
i
. We measure the Euclidian distance between a query and a data point
(CDistinLemma1)andthendeductthequeryrange.Lemma1captures
two cases of CDist. The ¯rst case (CDist(p
i
;q
j
)) computes a distance
p
i
f
0
= q
s
j
f in the worst-case scenario where both p
i
and q
j
move toward
s
j
q
e
j
q
x
i
p
s
k
q
e
k
q
y
j
T k
T x
f c c-kNN
range
f
j
r h
m
j
r
Fig.4. An adaptive safe region.
each other (under the constraint of the maximum speed). f
0
represents
the border point (on the border of q
j
:QR while q
j
arrives at f on its
movement segment), after which p
i
would possibly enter the query region
of q
j
. f is the closest point to q
s
j
on the trajectory of q
j
, which satis¯es
the condition that the distance from p
i
to f is equal to p
i
f
0
+f
0
f, where
f
0
f = q
j
:QR:radius = r
j
. Let p
i
f
0
= x for short. We can obtain the f
and f
0
points by computing x ¯rst, which is considered the safe distance
for p
i
with respect to q
j
. x can be easily computed with the trajectory
information of q
j
by solving the quadratic equation: (x + r
j
)
2
= h
2
+
(q
s
j
m¡ x)
2
(h is the height of triangle 4p
i
q
s
j
m). f on
¡ !
q
j
exists only
when µ
j
(\p
i
q
s
j
q
e
j
) is less or equal to
¼
2
and (p
i
q
e
j
¡q
j
:QR:radius)
¼
2
in the second case, the query range of q
j
can never cover p
i
due to the opposing movement of q
j
. In this example,
the safe distance x (with respect to q
j
) is smaller than y (with respect
to q
k
), so x is chosen as the radius of the adaptive safe region of p
i
. In
our system, since a c-kNN query can be considered an order-sensitive
range query, we use the same principle to compute safe regions for each
data object with respect to range queries and c-kNN queries. In case of a
query insertion or query region expansion of a c-kNN query, the adaptive
safe regions of the a®ected data objects must be reassigned according to
current queries to avoid any missing location updates.
3.2 Query Evaluation with Location Probes
The initial query results of the range and c-kNN queries are obtained
using CPM [4], and later the query results are updated in an event-
driven fashion. Such events include the insertion or update of a query.
In the following sections, we propose our incremental query re-evaluation
algorithms for both range and c-kNN queries. While updating the query
answers, on-demand server-initiated location probes are issued whenever
any location ambiguity exists. Speci¯cally, the cost of updating c-kNN
queries is usually higher than updating range queries. The reason is that
a c-kNN search is an order-sensitive query. The system executes more
location updates to ensure the order of the result points. Furthermore,
to make sure that at least k result points are found for a c-kNN query,
the query region often needs to be enlarged in a situation where both
query and data objects are moving, which leads to more location probes.
In our approach, the strategy to handle such increasing unnecessary lo-
cation updates incurred from a c-kNN query is that the query processor
computes (k+n) NNs for a c-kNN query instead of evaluating exactly k
NNs. This approach helps to reduce the number of future query region
expansionstoretrievesu±cientNNsforthequeries.Sinceac-kNNquery
is treated as an order-sensitive range query, we adopt the same principle
that is used for a range query to ¯nd the new answer set in the current
query regions ¯rst. A query region is expanded only when there are less
than k NNs in the result set. Finally, an order-checking procedure is per-
formed to examine the order of the result points and determine necessary
location probes.
Query Result Updates for Range Queries The query processor
re-evaluates the range queries based on their current positions by the
same principles as evaluating the initial query results. The traditional
approach adopts the query region itself as the safe region for all the
result points in the region to reduce the number of location updates.
However,theapproachincursmorenetworkmessageswhenarangequery
changes its position frequently, because the system needs to inform the
result points of the new position of the query region to avoid missing
location updates. An alternative approach basically monitors the entire
set of result points to obtain the new correct results. However, such an
approachisnotscalablewhentherearelargenumbersofrangequeries.In
thispaper,weuseamoving region (MR)foreachresultpointtoestimate
the possible movement at the server side. The query processor sends the
on-demand location probes to those result points that might move out of
thecurrentqueryregions.AMR isindexedonthegridandtheboundary
increases at each time step by the maximum moving distance until the
result point is probed by the server. Since the number of result points are
relatively small, indexing MRs does not signi¯cantly increase the overall
serverworkload.InFigure5(a),whenq
1
movestoq
0
1
,thequeryprocessor
checks p
1
and p
5
, since their MRs intersect with q
0
1
:QR.
For a data point, in addition to its adaptive safe region, we also con-
siderthecurrentpossiblemovingboundarytoserveasanadditionalindi-
cator for the server to determine a necessary location probe. Continuing
the example in Figure 5 (a), the gray circle surrounding p
4
is its ASR,
and the dashed circles represent the possible moving boundaries (the ra-
dius is equal to the maximum moving distance since the last update of
p
4
) for di®erent time steps. p
4
is checked because its p
4
:ASR overlaps
with q
0
1
:QR. However, the server does not need to issue a location probe
since the current moving boundary does not overlap with q
0
1
:QR. p
0
6
is a
newly updated (p
6
moves out of its ASR) data point. The system also
needs to check whether its current position is in the query region of q
0
1
.
Algorithm 1 shows the pseudo code of the range query evaluation, where
q
0
j
istheupdatedqueryofq
j
.Lines1-7removepreviousresultpointsthat
are not in the the current query region q
0
j
:QR. Lines 2 and 4 compute the
mindist and maxdist between a query point and a result point, respec-
tively. If a result point with a MR is completely contained in the query
range, a location probe is ignored. In Line 10, if p
i
is a data point, the
server uses the radius of ASR or the maximum moving distance since the
last update, which ever is less to estimate its possible moving distance.
Query Result Updates for c-kNN Queries A c-kNN query is more
complicated since it is order-sensitive. An intuitive solution enlarges a
query region that covers at least all the previous result points (¯rst k
2
p
1
q
r r
1
p
3
p
4
p
4
p c ASR
MR
2
q
5
p
6
p c 6
p
1
q c ASR
(a) Result updates of a range query.
2
p
1
q
r r
1
p
3
p
4
p
1
q c 5
p
expanded query region
ASR
(b) Result updates of a c-kNN query.
Fig.5. Query result updates.
Algorithm 1 RangeQuery-Update(q
0
j
)
1: for (each d2qj:RangeNN) do
2: if (dist(d;q
0
j
)¡d:MR:radius)>q
0
j
:QR:radius) then
3: remove d
4: else if (dist(d;q
0
j
)+d:MR:radius)>q
0
j
:QR:radius) then
5: probe d and remove d if its current position is outside of q
0
j
:QR
6: end if
7: end for
8: for (each c2G, which overlaps with the q
0
j
:QR) do
9: for(eachobjectp
i
whichresidesincorwhose(1) ASR,or(2)MR overlapswith
it) do
10: let r = p
i
:MR:radius, if p
i
is a result point; else let r =
min(p
i
:ASR:radius;±¢t)
11: if (dist(pi;q
0
j
)¡r 0) do
6: if (B:size>0) then
7: setq
0
j
:QR:radius =dist(q
0
j
;V),whereV isthev
th
NNinB,ifB:size>=v.
Otherwise, set dist(q
0
j
;L), where L is the last object in B.
8: empty B
9: perform RangeQuery-Update(q
0
j
) that inserts un-visited, discarded objects
into B, if any
10: v =k+n¡q
0
j
:KNN:size
11: else
12: performCPM(q
0
j
)thatcheckstheobjectsinthesurroundingcellsofq
0
j
:QR,
until (k+n) objects are ful¯lled, and terminate the loop.
13: end if
14: end while
15: end if
16: sort q
0
j
:KNN by performing OrderCheck(q
0
j
:KNN) that issues necessary location
probes.
Proof: The proof is straightforward, since when the order of p
i
and p
i+1
changes,mindist(p
i
;q
0
j
)¸mindist(p
i+1
;q
0
j
).Whenconsideringtheworst
casethatp
i
movesinanopposingdirectionfromq
0
j
andp
i+1
movestoward
q
0
j
directly, the following inequality holds true:
mindist(p
i
;q
0
j
)+`¸mindist(p
i+1
;q
0
j
)¡`
Therefore, we conclude that the order of p
i
and p
i+1
must change, when
`¸(mindist(q
0
j
;p
i+1
) - mindist(q
0
j
;p
i
))£
1
2
. It is necessary for the server
to probe both locations of p
i
and p
i+1
.
In Figure 6, the result set of q
0
1
is fp
2
;p
1
;p
3
g sorted by the distance
between q
0
1
and their positions at the server since the last updates. The
OrderCheck procedure ¯rst checks p
2
and p
1
. Since dist(q
0
1
;p
2
) +r
2
>
1
p
2
p
3
p
1
q c x y
1
r
2
r
3
r
2
p c 1
p c 1
q
Fig.6. The order checks of a c-kNN query.
dist(q
0
1
;p
1
)¡r
1
, the order of p
2
and p
1
might need to be switched. The
system needs to probe p
2
and p
1
. After the location probes, the order of
the NNs becomes fp
0
1
;p
0
2
;p
3
g. Thus, the procedure checks the next pair
of p
0
2
and p
3
. Since dist(q
0
1
;p
0
2
) < dist(q
0
1
;p
3
)¡r
3
, the location probe of
p
3
is not necessary.
4 Experimental Evaluation
We evaluated the performance of the proposed framework that utilizes
ASRs and compared it with the traditional safe region approach [4,9]
andaperiodicupdateapproach(PER).Theperiodictechniquefunctions
as a baseline algorithm where each object issues a location update (only
uplinkmessagesareissuedinthisapproach)everytimeitmovestoanew
position.Weextendedthesaferegionapproach(SR*)tohandledynamic
range and c-kNN queries where the result points are monitored the same
wayasinASR.Wepreservethetraditionalsaferegioncalculations(max-
imum non-overlapping area) for the SR* approach. The simulation steps
andthedetailedsimulationresultsaredescribedinthefollowingsections.
4.1 Simulation Steps
We use a main memory grid as the underlying index structure for all the
three approaches. Our data sets are generated on a terrain service space
of [0;1024]
2
. We assume a maximum speed for any moving object in the
range of [0:48;1:25]. The mobility (the percentage of objects that move
from time step to time step) for the objects is set in a range from 10% to
50%. The length q
len
of a range query is set in the range of [1,10] and k
for the a kNN query is set from 5 up to 20. In the simulations, the main
measurement is the cost of the communication overhead which includes
uplink messages (e.g., a mobile-initiated location update) and downlink
messages(e.g.,aserver-initiatedlocationprobe).Thecommunicationcost
is measured by assuming that the cost of an uplink message (c
up
= 2) is
twice as costly as a downlink message (c
down
= 1). Table 2 summarizes
the default parameter settings in the following simulations.
Parameter Default Range
Number of objects (P) 100K 50K, 100K, 150K, 200K
Number of queries (Q) 100 50, 100, 150, 200
Mobility rate 50% 10%, 20%,30%, 40%, 50%
Number of NNs (K) 10 5, 10, 15, 20
Querylengthforrangequeries(q
len
) 5 1, 5, 10
Table 2. Simulation parameters
4.2 Number of Extra NNs
First, we test the e±ciency of using extra NNs (n) for c-kNN queries by
varying the number of n, since this factor greatly a®ects the number of
downlink messages. The choice of the number of extra NNs is a trade-o®.
If n is too large, the query processor evaluates more NNs for a query
and the system is more likely to issue more location probes since a larger
query region might overlap with more data objects for location probes. If
n is too small, there are more query expansions which might also cause
location probes. Figure 7 shows the number of overall communication
cost (measured in thousands of messages) as a function of the number
of extra NNs ranging from 0 to 20. When n is set to more than 10, the
performance of ASR is degraded in terms of the communication cost.
Therefore, we chose n=10 for the rest of our experiments as this setting
results in reduced communication cost.
7
7.5
8
8.5
9
0 5 10 15 20
Communication Cost (K)
Number of extra NNs (n)
ASR
Fig.7. Extra NNs v.s. communication cost.
4.3 Cardinality
Weexaminedthee®ectofthequeryandobjectcardinalityassumingthat
all query and object sets move with a mobility rate of 50%. Figure 8 (a)
shows the communication overhead of ASR, SR* and PER with respect
to the object cardinality. ASR outperforms SR* and PER. The di®er-
ence increases as the number of objects grows. Since an ASR reconciles
the surrounding moving queries, a query movement does not incur many
unnecessary location probes from the surrounding objects. SR* on the
other hand, triggers many location probes from the objects whose safe
regions overlap with a query region once the query changes its position.
As the density of objects increases, there are more objects in the vicinity
area of a query region. Hence SR* incurs an increasing number of loca-
tion updates as the cardinality increases. Figure 8 (b) shows the impact
of the number of queries. Our algorithm achieves about 50% reduction
compared with SR* and 90% reduction compared with PER.
20
40
60
80
100
120
50k 100k 150k 200k
Communication cost (K)
Number of objects
ASR
SR*
PER
(a) P v.s. communication cost.
10
20
30
40
50
60
70
80
90
100
50 100 150 200
Communication cost (K)
Number of queries
ASR
SR*
PER
(b) Q v.s. communication cost.
Fig.8. Object and query cardinality.
4.4 Query Coverage
ThequerycoveragevarieswiththenumberofNNs(forkNNqueries)and
the query length (for range queries). Figure 9 (a) shows the communica-
tion cost as a function of the number of NNs and Figure 9 (b) illustrates
the e®ect of the query length. Overall, the communication cost increases
as a function of k and q
len
. However, since ASR and PER utilize the
OrderCheck procedure to reduce the number of location probes from the
objects which do not violate the order of result sets, the communication
overhead remains stable when k increases. This con¯rms the feasibility
of the OrderCheck procedure as well as the c-kNN update mechanisms
of our approach. The PER approach basically monitors all the moving
objects. Therefore, the number of k is irrelevant to the communication
cost; however, PER is not scalable when there is high query coverage.
10
20
30
40
50
60
70
80
90
100
5 10 15 20
Communication cost (K)
k of c-kNN queries
ASR
SR*
PER
(a) k v.s. communication cost.
10
20
30
40
50
60
70
80
90
100
1 5 10
Communication cost (K)
Lenth of range queries
ASR
SR*
PER
(b) q
len
v.s. communication cost.
Fig.9. E®ect of query coverage with k and q
len
.
4.5 Mobility
Finally, we evaluated the impact of the mobility rate. Figures 10 (a) and
(b) show the communication cost as a function of the object and query
mobility, respectively. The ASR approach achieves a reduced location
update rate compared to the other two approaches for all mobility rates.
PER and SR* have worse performance in terms of communication cost
when the mobility rate is high. The degradation is caused by the location
probes due to query movements.
10
20
30
40
50
60
70
80
90
100
10 20 30 40
Communication cost (K)
Mobility of objects
ASR
SR*
PER
(a) Object mobility v.s. communica-
tion cost.
10
20
30
40
50
60
70
80
90
100
10 20 30 40
Communication cost (K)
Mobility of queries
ASR
SR*
PER
(b) Query mobility v.s. communica-
tion cost.
Fig.10. Object and query mobility.
5 Conclusions
We have designed an ASR-based framework for highly dynamic environ-
ments where mobile units may freely change their locations. The novel
conceptofanadaptivesaferegionisintroducedtoprovideamobileobject
withareasonable-sizedsaferegionthatadaptstothesurroundingqueries.
Hence, the communication overhead resulting from the query movements
is greatly reduced. To further decrease network tra±c caused by c-kNN
query region expansions to cover su±cient NNs for the result sets, our
approach caches extra NNs. An incremental result update mechanism
that checks only the set of a®ected points to refresh the query answers
is presented. Experimental results demonstrate that our approach scales
better than existing techniques in terms of the communication cost and
the outcome con¯rms the feasibility of the ASRs approach.
References
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Description

Yu-Ling Hsueh, Roger Zimmermann, Wei-Shinn Ku. "An enhanced safe region technique for continuous queries over moving objects." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 909 (2009).

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Creator Hsueh, Yu-Ling (author), Ku, Wei-Shinn (author), Zimmermann, Roger (author)

Core Title USC Computer Science Technical Reports, no. 909 (2009)

Alternative Title An enhanced safe region technique for continuous queries over moving objects (title)

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