outline - sstd 2011

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Online Computation of Fastest Path in Online Computation of Fastest Path in TimeTime--Dependent Spatial NetworksDependent Spatial Networksp pp p

Ugur DemiryurekUgur Demiryurek11, , FarnoushFarnoush BanaeiBanaei--KashaniKashani11, , Cyrus ShahabiCyrus Shahabi11, and , and AnandAnand RanganathanRanganathan22

University of Southern CaliforniaUniversity of Southern California11

and IBM T.J. Watson Research Centerand IBM T.J. Watson Research Center22

Outline

MotivationMotivationProblem DefinitionProblem DefinitionRelated WorkRelated WorkTimeTime--dependent Fastest Path Computationdependent Fastest Path ComputationPerformance EvaluationPerformance Evaluation

2

Conclusion and Future WorkConclusion and Future Work

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Motivation

What is the fastest path to

?

• Growing Popularity of Online Map Services

100 Million hits per month (http://googlemobile.blogspot.com/)

Which

?

What is the fastest path to

? is nearby??

Road networks can be very large, e.g., 45M segments for North America

Motivation•• Existing FP and FP Existing FP and FP PrecomputationPrecomputation Techniques Techniques

–– Based on the Based on the constant constant edge weights for each edgeedge weights for each edge

The path recommendation from online map applications remains the same throughout the day regardless of the departure-time from the source (i.e., query time)

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Motivation•• Existing FP and FP Existing FP and FP PrecomputationPrecomputation Techniques Techniques

–– Based on the Based on the constant constant edge weights for each edgeedge weights for each edge

•• In RealIn Real worldworld•• In RealIn Real--worldworld–– The weight of an edge is a function of time, i.e.,The weight of an edge is a function of time, i.e., timetime--dependent.dependent.–– ArrivalArrival--time to an edge determines the traveltime to an edge determines the travel--time on that edgetime on that edge..

5:00 PM8 :30 AM

Monday travel‐time on a segment of I‐10 in LA (generated based on two years of historical traffic sensor data)

Pictures courtesy : http://www.wfrc.org/cms

Motivation•• TimeTime--dependent Fastest Pathdependent Fastest Path

–– Recommends different paths for different departureRecommends different paths for different departure--timestimes

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Outline

MotivationMotivationProblem DefinitionProblem DefinitionRelated WorkRelated WorkTimeTime--dependent Fastest Path dependent Fastest Path ComputationComputation

7

Performance EvaluationPerformance EvaluationConclusion and Future WorkConclusion and Future Work

Problem Definition

s

•• Given a timeGiven a time--dependent spatial network dependent spatial network where where edge weights are function of timeedge weights are function of time

wij(t)

Source s and Destination d

Time-dependent Fastest Path (TDFP)

sij( )

t

w3

w1

w2

d

TDFP (s, d, t_s) with respect to s, d and query time t_s finds minimum travel time path among all paths between s and d

Travel-time from s to any destination is time-dependent, i.e., changes based on the departure time.

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t6 n4

Problem Definition

t2

t5

4n3

n4

n4

Path={n1,n3,n4}, Cost=6Path={n1,n2,n4}, Cost=5

SP={n1,n2,n4}

t0

2 1

22

n4

n3

n2

n1

3n2

Path={n1,n3,n4}, Cost=3

Challenges•• Input Size for Precomputation: Input Size for Precomputation:

–– SuperSuper--polynomial number of shortest polynomial number of shortest pp p yp ypaths between any pair of nodespaths between any pair of nodes

n4

t

w12(t), w34(t)

( )

5

w24(t)

10

15

15

t

( )

n2

n1

n2

n1 n4

n

source destination

–– The shortest path The shortest path is not unique in TDis not unique in TD--SN SN and changes with the departure timeand changes with the departure time

–– Recall:SPRecall:SP is unique in static road networks.is unique in static road networks.–– The The lowerlower--envelopeenvelope can have can have super-

polynomial pieces [Dean’04,Foschini’11]pieces [Dean’04,Foschini’11]28

35

fp3fp1

fp2fpi (cost)

204

w23(t)

15

25

825

w13(t)

10

tt

n3

1n3

fp1=f24(f12(t)) fp2=f34(f23(f12(t)))fp3=f34(f13(t))

p y p [ , ]p [ , ]

fpi : total traveltotal travel--time to destinationtime to destination3 10 20

17

t (departure time)

15

7

t : depature time

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Challenges•• Availability of the timeAvailability of the time--dependent dependent

edge weights (i.e., traveledge weights (i.e., travel--time) datatime) data–– NavteqNavteq and and TeleatlasTeleatlas

•• Recently released the timeRecently released the time--dependent traveldependent travel--times for road times for road networks in North Americanetworks in North America

–– Government Agencies Government Agencies •• LA Metro and USC (LA Metro and USC (MetransMetrans andand•• LA Metro and USC (LA Metro and USC (MetransMetrans and and

IMSC) IMSC)

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Outline


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Related Work

TD R d N kS i R d N k

Shortest Path

TD-Road NetworkStatic Road Network

• Dijkstra

• A* Precomputation:•Geometric speed-up techniques for finding SP, [Wagner et al.,ESA'03]

•A* Search Meets Graph Theory [Goldberg,SODA’05]

•Engineering fast route planning algorithms, [Sanders et al., WEA’07]

• Hierarchical routing in road networks [Geisberger et al WEA’08 Sanders ESA’06]Hierarchical routing in road networks, [Geisberger et al., WEA 08, Sanders ESA 06]

•Scalable network distance browsing [Samet et al., SIGMOD’08]

Related Work

TD R d N k

Shortest Path

S i R d N k TD-Road Network

• Dreyfus [OR’69] (Dijkstra Variant)

• Orda and Rom, [JACM’90] (Bellman F.)

• George and Shekhar [SSTD’07] (TAG)

• Time-dependent SHARC [ Delling et al., ESA’08]

• Time-dependent CH [Batz et al., ALENEX’08]

Precomputation:

Static Road Network

• Time-dependent ALT [Nannicini et al., WEA’09]

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Outline


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TD Fastest Path

•• Generalize A* algorithm proposed for static spatial Generalize A* algorithm proposed for static spatial networks to timenetworks to time--dependent road networksdependent road networksnetworks to timenetworks to time dependent road networksdependent road networks

•• Dijkstra vs. A* Dijkstra vs. A*

d

ssA* SearchDijkstraDijkstra

d

16

increasing cost s

d

h(v) =(vi,d) vivj

Optimality Condition:h(v) should not overestimate the actual distance between v and d

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TD Fastest Path•• Generalize A* algorithm proposed for static spatial networks to timeGeneralize A* algorithm proposed for static spatial networks to time--

dependent road networksdependent road networks

sd Bidirectional

A* Algorithm

Time-dependent bidirectional A* is not straight forward:Challenge 1: The distance between any node v and d is time-dependent, hence need a good h(v) Challenge 2: Start the backward search from the arrival-time at the destination td , but td cannot be determined at the query time

TD Fastest Path

•• Proposed solution: Proposed solution: PrecomputationPrecomputation Phase:Phase:–– PrecomputationPrecomputation Phase: Phase:

•• Partition the road network into nonPartition the road network into non--overlapping overlapping partitions partitions

•• Precompute Precompute lowerlower--bound intra and inter bound intra and inter distance labels distance labels within and across the partitionswithin and across the partitions

–– Online Phase: Online Phase: •• Use the Use the precomputedprecomputed distance labels as a heuristic distance labels as a heuristic

function in the bidirectional timefunction in the bidirectional time--dependent A* dependent A* searchsearch

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TD Fastest Path: Precomputationwij(t) Upper-bound

travel time s

• TD Spatial Network Property

•• TimeTime--independentindependent GraphsGraphs

t

t a e t ew3

Lower-bound travel time

w1

s

dTDFP (s,d,t)

pp pp–– LowerLower--bound Graph bound Graph –– G G , LTT, LTT

•• where edge weights are minimum possible weights where edge weights are minimum possible weights

–– UpperUpper--bound Graphbound Graph-- G , UTTG , UTT•• where edge weights are maximum possible weights where edge weights are maximum possible weights

DLTT(q,p)< TDSP(q,p,t)<DUTT(q,p)

TD Fastest Path: Precomputation

•• Partition the road network to nonPartition the road network to non--overlapping partitions overlapping partitions [Gonzalez, VLDB’07][Gonzalez, VLDB’07]

S1 S2S3

S4S5

S6S7

S10

[Gonzalez, VLDB 07][Gonzalez, VLDB 07]

Border Nodes

S8S9 S11

Our algorithm yields correct results with all non-overlapping partitioning algorithms

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•• Compute Compute intra and inter distance labels intra and inter distance labels within and within and across the partitions based onacross the partitions based on LowerLower--bound Graphbound Graph GGacross the partitions based on across the partitions based on LowerLower bound Graphbound Graph GG

S d

b1

b2

b3

b4

S1 S2

• Only store the minimum of nodeOnly store the minimum of node--toto--border, borderborder, border--toto--border, border, and borderand border--toto--node travel timesnode travel times

h(s) = LTT (s, b1) + LTT (b1, b3) + LTT (b4, d) <= TDSP(s,d,ts) Challenge 1


Node Partition Node-to-Border

Border-to-Node

Border Border Distance Distance

• Distance Labels

Border Noden1 S1 b1,5 b1,7

n2 S1 b2,6 b3,4

…. …. …. ….

n41 S9 b17,3 b15,6

nn Sk bu,,x bv,y

b1 b3 14 12

b1 b4 18 15

b1 b15 12 9

…. …. ….

bn bk x y

Node-to-Border (Intra) Border-to-Border (Inter)

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TD Fastest Path

•• Bidirectional TimeBidirectional Time--dependent A* dependent A* –– Forward Search: TimeForward Search: Time--dependent A* using h(v) found based ondependent A* using h(v) found based on–– Forward Search: TimeForward Search: Time--dependent A using h(v) found based on dependent A using h(v) found based on

distance labels distance labels –– Backward Search : TimeBackward Search : Time--independent A* based on the reverse independent A* based on the reverse

lowerlower--bound graph bound graph GG . Note: h(v) is still valid . Note: h(v) is still valid

s dTDSP(s,u,ts) LTT(u,d)

u

Challenge 2

Cannot stop! TDSP(Cannot stop! TDSP(s,u,ts,u,tss)+ LTT()+ LTT(uu dd, , ttuu) < TDSP() < TDSP(s,d,ts,d,tss))

TD Fastest Path



lowerlower--bound graph bound graph GG . Note: h(v) is still valid. . Note: h(v) is still valid.

s dTDSP(s,u,ts) LTT(u,d)

u

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TD Fastest Path



lowerlower--bound graph bound graph GG . Note: h(v) is still valid. . Note: h(v) is still valid.

s d

TDSP( d t )TDSP(s,d,ts)

Continue the search only within the nodes found by backward search Continue the search only within the nodes found by backward search (see Section:5.2)(see Section:5.2)

Outline


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Experimental Evaluation• DataSetsDataSets: : (obtained from (obtained from NavteqNavteq))

•• Los Angeles (LA) road network, Los Angeles (LA) road network, 304304,,162 162 nodesnodesnodes nodes •• California (CA) road network, California (CA) road network, 11,,965965,,300 300 nodes nodes

• Experimental Setup:•• A server with A server with 22..7 7 GHz Pent. Duo Core GHz Pent. Duo Core

Proc. and Proc. and 1212GB RAMGB RAM•• Source s destination d and departureSource s destination d and departure

27 /38

•• Source s, destination d and departure Source s, destination d and departure time time ttss are determined uniformly at randomare determined uniformly at random

•• Average results computed from Average results computed from 1000 1000 random srandom s--d queries d queries

Experimental Evaluation

•• TimeTime--dependent Data dependent Data GenerationGenerationGenerationGeneration–– 6500 Sensors on freeways and 6500 Sensors on freeways and

arterials in LAarterials in LA•• 1 sensor/reading per minute 1 sensor/reading per minute •• Collecting and archiving past 2 Collecting and archiving past 2

years years

–– Spatially and temporally aggregateSpatially and temporally aggregateSpatially and temporally aggregate Spatially and temporally aggregate the sensor data by assigning the sensor data by assigning interpolation points (for each 5 interpolation points (for each 5 minutes)minutes)

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•• Comparison with TDComparison with TD--ALTALT–– TDTD--ALT: Determine 64ALT: Determine 64TDTD ALT: Determine 64 ALT: Determine 64

landmarks based on landmarks based on maxCovermaxCover(best known landmark selection (best known landmark selection algorithm) algorithm)

–– TDFP: Divide CA network to 60 TDFP: Divide CA network to 60 partitions partitions

Storage:Storage:

•

Response Time:TD-ALT very loose bounds based on therandomly selected s and d, and hencethe large search space.

Storage: Storage: • TD-ALT attaches each node an array of 64 elements. Total Storage = 63 MB for CA

• TDFP consumes, for each node, an array of 2 elements + border-to-border distance labels. Total Storage=8.5 MB for CA


•• SpeedSpeed--up up vsvs Distance Distance •• LowerLower--bound Qualitybound QualityUnidirectional vs Bidirectional wrt

lowerlower--bound quality = bound quality = δ(δ(u,vu,v)/ d()/ d(u,vu,v))

N ïN ï dd (( )/)/ dd

Unidirectional vs Bidirectional wrtdistance between s and d?

Naïve: Naïve: ddeuceuc((u,vu,v)/ )/ max_speedmax_speedALT:ALT: Landmark based Landmark based DL: DL: Distance label based Distance label based

Speed-up is significantly more especially for long distance queries

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Experimental Evaluation•• More Comparison More Comparison

Outline


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Conclusion•• From static road networks to more realistic timeFrom static road networks to more realistic time--dependent road dependent road

networks where edge weights are timenetworks where edge weights are time--varyingvarying•• PrePre--computation is challenging in timecomputation is challenging in time--dependent road networks dependent road networks

(Super(Super--polynomial input size)polynomial input size)•• Proposed TimeProposed Time--dependent bidirectional A* based on inter and intra dependent bidirectional A* based on inter and intra

distance labelsdistance labels•• Plan to work on Plan to work on

–– Incremental algorithms to support rapid network edge weight Incremental algorithms to support rapid network edge weight changes (e.g., due to accidents)changes (e.g., due to accidents)changes (e.g., due to accidents)changes (e.g., due to accidents)

–– Better bounds to expedite the searchBetter bounds to expedite the search–– Different network Different network partitioning techniques partitioning techniques

References•• S. E. Dreyfus. An appraisal of some shortestS. E. Dreyfus. An appraisal of some shortest--path algorithms. In Operations Research Vol. 17, No. 3, 1969.path algorithms. In Operations Research Vol. 17, No. 3, 1969.•• G. V. G. V. BatzBatz, D. , D. DellingDelling, P. Sanders, and C. Vetter. Time, P. Sanders, and C. Vetter. Time--dependent contraction hierarchies. In ALENEX, 2009.dependent contraction hierarchies. In ALENEX, 2009.•• L. Cooke and E. Halsey. The shortest route through a network with L. Cooke and E. Halsey. The shortest route through a network with timedependenttimedependent internodalinternodal transit times. In transit times. In

Journal of Mathematical Analysis and Applications, 1966.Journal of Mathematical Analysis and Applications, 1966.•• B. C. Dean. Algorithms for minimumB. C. Dean. Algorithms for minimum--cost paths in timecost paths in time--dependent networks with waiting policies. In Networks,2004.dependent networks with waiting policies. In Networks,2004.•• D. D. DellingDelling. Time. Time--dependent dependent sharcsharc--routing. In ESA, 2008. routing. In ESA, 2008. •• D. D. DellingDelling and D. Wagner. Landmarkand D. Wagner. Landmark--based routing in dynamic graphs. In WEA, 2007based routing in dynamic graphs. In WEA, 2007..•• G.NanniciniG.Nannicini et al. Bidirectional et al. Bidirectional A Search for A Search for TimeTime--Dependent Fast Paths. In EA’2008Dependent Fast Paths. In EA’2008•• J. J. HalpernHalpern. Shortest route with time dependent length of edges and limited delay in nodes. In MMO, 1969. . Shortest route with time dependent length of edges and limited delay in nodes. In MMO, 1969. •• E. E. KanoulasKanoulas, Y. Du, T. Xia, and D. Zhang. Finding fastest paths on networks with speed patterns. In ICDE, 2006., Y. Du, T. Xia, and D. Zhang. Finding fastest paths on networks with speed patterns. In ICDE, 2006.•• E. E. KöhlerKöhler, K. , K. LangkauLangkau, and M. , and M. SkutellaSkutella. Time. Time--expanded graphs for flowexpanded graphs for flow--dependent transit times. In ESA, 2002.dependent transit times. In ESA, 2002.•• U. U. LautherLauther. An extremely fast, exact algorithm for finding shortest paths in static networks with geographical . An extremely fast, exact algorithm for finding shortest paths in static networks with geographical

background. In background. In GeoinformationGeoinformation and and MobilitatMobilitat, 2004., 2004.•• NAVTEQ. http://www.navteq.com, Accessed in May 2010.NAVTEQ. http://www.navteq.com, Accessed in May 2010.NAVTEQ. http://www.navteq.com, Accessed in May 2010.NAVTEQ. http://www.navteq.com, Accessed in May 2010.•• A. A. OrdaOrda and R. Rom. Shortestand R. Rom. Shortest--path and minimumpath and minimum--delay algorithms in networks with timedelay algorithms in networks with time--dependent edgedependent edge--length. length.

J.ACM, 1990.J.ACM, 1990.•• H. H. SametSamet, J. , J. SankaranarayananSankaranarayanan, and H. , and H. AlborziAlborzi. Scalable network distance browsing in spatial databases. In . Scalable network distance browsing in spatial databases. In

SIGMOD, 2008.SIGMOD, 2008.•• P. Sanders and D. P. Sanders and D. SchultesSchultes. Highway hierarchies hasten exact shortest path queries. In ESA, 2005.. Highway hierarchies hasten exact shortest path queries. In ESA, 2005.•• P. Sanders and D. P. Sanders and D. SchultesSchultes. Engineering fast route planning algorithms. In WEA, 2007.. Engineering fast route planning algorithms. In WEA, 2007.•• TELEATLAS. http://www.teleatlas.com, Accessed in May2010.TELEATLAS. http://www.teleatlas.com, Accessed in May2010.•• D. Wagner and T. D. Wagner and T. WillhalmWillhalm. Geometric speed. Geometric speed--up techniques for finding shortest paths in large graphs. In ESA, 2003.up techniques for finding shortest paths in large graphs. In ESA, 2003.

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References•• H.H.--J. Cho and C.J. Cho and C.--W. Chung. An W. Chung. An ecientecient and scalable approach to and scalable approach to cnncnn queries in a road network. In VLDB, 2005.queries in a road network. In VLDB, 2005.•• E. G. E. G. HoelHoel and H. and H. SametSamet. . EcientEcient processing of spatial queries in line segment databases. In SSD, 1991.processing of spatial queries in line segment databases. In SSD, 1991.•• M. M. KolahdouzanKolahdouzan and C. and C. ShahabiShahabi. Voronoi. Voronoi--based k nearest neighbor search for spatial network databases. In VLDB, based k nearest neighbor search for spatial network databases. In VLDB,

2004.2004.•• M. R. M. R. KolahdouzanKolahdouzan and C. and C. ShahabiShahabi. Continuous k. Continuous k--nearest neighbor queries in spatial network databases. In nearest neighbor queries in spatial network databases. In

STDBM, 2004.STDBM, 2004.•• U. U. LautherLauther. An extremely fast, exact algorithm for . An extremely fast, exact algorithm for ndingnding shortest paths in static networks with geographical shortest paths in static networks with geographical

background. In background. In GeoinformationGeoinformation and and MobilitatMobilitat, 2004., 2004.•• M. F. M. F. MokbelMokbel, X. , X. XiongXiong, and W. G. , and W. G. ArefAref. . SinaSina: scalable incremental processing of continuous queries in : scalable incremental processing of continuous queries in spatiospatio--

temporal databases. In SIGMOD, 2004.temporal databases. In SIGMOD, 2004.•• K. K. MouratidisMouratidis, D. , D. PapadiasPapadias, and M. , and M. HadjieleftheriouHadjieleftheriou. Conceptual partitioning: an . Conceptual partitioning: an ecientecient method for continuous method for continuous

nearest neighbor monitoring. In SIGMOD, 2005.nearest neighbor monitoring. In SIGMOD, 2005.•• K. K. MouratidisMouratidis, M. L. , M. L. YiuYiu, D. , D. PapadiasPapadias, and N. , and N. MamoulisMamoulis. Continuous nearest neighbor monitoring in road networks. . Continuous nearest neighbor monitoring in road networks.

In VLDB, 2006.In VLDB, 2006.DD PapadiasPapadias J Zhang NJ Zhang N MamoulisMamoulis and Y Tao Query processing in spatial network databases In VLDB 2003and Y Tao Query processing in spatial network databases In VLDB 2003•• D. D. PapadiasPapadias, J. Zhang, N. , J. Zhang, N. MamoulisMamoulis, and Y. Tao. Query processing in spatial network databases. In VLDB, 2003., and Y. Tao. Query processing in spatial network databases. In VLDB, 2003.

•• S. J. Russell and P. S. J. Russell and P. NorvigNorvig. . ArticialArticial intelligence: A modern approach. Prenticeintelligence: A modern approach. Prentice--Hall, Inc., 1995.Hall, Inc., 1995.•• C. C. ShahabiShahabi, M. R. , M. R. KolahdouzanKolahdouzan, and M. , and M. SharifzadehSharifzadeh. A road network embedding technique for k. A road network embedding technique for k--nnnn search in search in

moving object databases. moving object databases. GeoinformaticaGeoinformatica, 2003., 2003.•• Z. Song and N. Z. Song and N. RoussopoulosRoussopoulos. K. K--nearest neighbor search for moving query point. In SSTD, 2001.nearest neighbor search for moving query point. In SSTD, 2001.•• Y. Tao and D. Y. Tao and D. PapadiasPapadias. Time. Time--parameterized queries in parameterized queries in spatiospatio--temporal databases. In SIGMOD, 2002.temporal databases. In SIGMOD, 2002.

References•• Y. Tao, D. Y. Tao, D. PapadiasPapadias, and Q. , and Q. ShenShen. Continuous nearest neighbor search. In VLDB, 2002. Continuous nearest neighbor search. In VLDB, 2002•• H. X., J. C.S., H. L., and S. H. X., J. C.S., H. L., and S. SaltenisSaltenis. S. S--grid: A versatile approach to grid: A versatile approach to ecientecient query processing in spatial networks. In query processing in spatial networks. In

SSTD, 2007.SSTD, 2007.•• H. X., J. C.S., and S. H. X., J. C.S., and S. SaltenisSaltenis. The island approach to nearest neighbor querying in spatial networks. In SSTD, . The island approach to nearest neighbor querying in spatial networks. In SSTD,

2005.2005.•• X. X. XiongXiong, M. F. , M. F. MokbelMokbel, and W. G. , and W. G. ArefAref. Sea. Sea--cnncnn: Scalable processing of continuous k: Scalable processing of continuous k--nearest neighbor queries in nearest neighbor queries in

spatiospatio--temporal databases. In ICDE, 2005.temporal databases. In ICDE, 2005.•• X. Yu, K. Q. X. Yu, K. Q. PuPu, and N. , and N. KoudasKoudas. Monitoring k. Monitoring k--nearest neighbor queries over moving objects. In ICDE, 2005.nearest neighbor queries over moving objects. In ICDE, 2005.•• J. Zhang, M. Zhu, D. J. Zhang, M. Zhu, D. PapadiasPapadias, Y. Tao, and D. L. Lee. Location, Y. Tao, and D. L. Lee. Location--based spatial queries. In SIGMOD, 2003.based spatial queries. In SIGMOD, 2003.•• B. B. ZhengZheng and D. L. Lee. Semantic caching in locationand D. L. Lee. Semantic caching in location--dependent query processing. In SSTD, 2001.dependent query processing. In SSTD, 2001.

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outline - sstd 2011

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