Evaluating Queries over Route Collections Panagiotis Bouros, PhD defense.

Evaluating Queries over Route Collections

Panagiotis Bouros, PhD defense

Outline Introduction

Route collections examples Query evaluation challenges

Evaluating path queries Dynamic Pickup and Delivery with Transfers Most Trusted Near Shortest Path Conclusions Future work

June 30, 2011PhD defense

Routes as data Several applications involve storing and

querying large volumes of sequential data Route, a sequence of spatial locations

POIs, waypoints etc. Route collection

Routes as first-class citizens Frequently updated

New routes added Existing routes deleted or modified


Example 1: Sightseeing and activities People visit Athens

GPS devices Track sightseeing Touristic routes

Route collections online www.ShareMyRoutes.co

m www.TravelByGPS.com

Updates Add new interesting

routes Remove existing routes,

not interesting any more


Example 1: Sightseeing and activities Traditional graph queries

REACH: Is there a sequence of POIs from Academy to Zappeion?

PATH: Find a sequence of POIs from Academy to Zappeion

PATH more general Graph-based solution

Searching Low maintenance cost Slow

Compressing TC Fast High maintenance cost

This thesis Combine pros and cons Reachability within routes


Example 1: Sightseeing and activities Traditional graph queries

REACH: Is there a sequence of POIs from Academy to Zappeion?

PATH: Find a sequence of POIs from Academy to Zappeion

PATH more general Graph-based solution

Searching Low maintenance cost Slow

Compressing TC Fast High maintenance cost

This thesis Combine advantages Reachability within routes


Example 2: Pickup and delivery A courier company

offering pickup and delivery services

Static plan Set of requests Transfers between

vehicles Collection of vehicles

routes Pickup and Delivery with

Transfers Create static plan

Updates Ad-hoc requests Modify vehicle routes to

satisfy new requests


Example 2: Pickup and delivery


Query Pickup object from ns and

delivery at nt Minimize company’s

expenses dynamic Pickup and

Delivery with Transfers Non-graph solution

Two-phase local search This thesis

First work target dPDPT Cost metrics

Company’s viewpoint, extra traveling or waiting time

Customer’s viewpoint, delivery time

Dynamic two-criterion shortest path problem

Example 2: Pickup and delivery


Query Pickup object from ns and

delivery at nt Minimize company’s

expenses dynamic Pickup and

Delivery with Transfers Non-graph solution

Two-phase local search This thesis

First work for dPDPT Cost metrics

Company’s viewpoint, extra traveling or waiting time

Customer’s viewpoint, delivery time

Dynamic two-criterion shortest path problem

Example 3: Driving data Group of people driving through the city

Track their driving Vehicle routes

Sequence of road network intersections

Collection of vehicle routes A trusted and familiar way of driving People consult collection

Updates New routes added - driving to unknown locations Existing routes modified – new ways to reach

known locations


Example 3: Driving data Query

Driving directions from ns to nt

Graph-based solution Shortest path Time-dependent shortest path

This thesis Capture how people actually drive

Tend to reuse roads Consult friends Prefer a trusted over the fastest way

New graph query Most Trusted Near Shortest Path

Cost metrics Unknown time, time outside routes Length, total time

Path with lowest unknown time and length at most a times larger than SP


Example 3: Driving data Query

Driving directions from ns to nt

Graph-based solution Shortest path Time-dependent shortest path

This thesis Capture how people actually drive

Tend to reuse roads Consult friends Prefer a trusted over the fastest way

Cost metrics Unknown time, time outside routes Length, total time

New graph query Most Trusted Near Shortest Path Path with lowest unknown time and length at most a times larger than

SP


Query evaluation Frequent updated route collections available Challenge for query evaluation

Path queries Sequence of locations contained in routes

Evaluate queries directly on routes Is it faster? Route as a set of precomputed answers


Outline Introduction

Route collections examples Query evaluation challenges

Evaluating path queries Dynamic Pickup and Delivery with Transfers Most Trusted Near Shortest Path Conclusions Future work


Evaluating path queries


Evaluating PATH queries Query

PATH(ns,nt)

Solution Answer: a sequence of locations in routes from ns

to nt

Indexing route collections Route traversal paradigm Link traversal paradigm Methods for index maintenance


Indexing route collections R-Index

Associates each location of the collection with the routes containing it

T-Index Captures all possible

transitions between routes via links Links are shared nodes

location

routes[] list

a ⟨r2:3⟩,⟨r3:3⟩

s ⟨r1:5⟩,⟨r3:1⟩,⟨r5:2⟩

t ⟨r1:4⟩,⟨r5:1⟩

… …

r1 (d,f,y,t,s)

r2 (v,b,a,c,d,x)

r3 (s,w,a,g)

r4 (b,z,c,f)

r5 (t,s)June 30, 2011PhD defense

route

trans[] list

r2 ⟨r1,d:5:1⟩,⟨r3,a:3:3⟩,⟨r4,b:2:1⟩,⟨r4,c:4:3⟩

r3 ⟨r1,s:1:5⟩,⟨r2,a:3:3⟩,⟨r5,s:1:2⟩

… …

Indexing route collections R-Index

Associates each location of the collection with the routes containing it

T-Index Captures all possible

transitions between routes via links Links are shared nodes

location

routes[] list

a ⟨r2:3⟩,⟨r3:3⟩

s ⟨r1:5⟩,⟨r3:1⟩,⟨r5:2⟩

t ⟨r1:4⟩,⟨r5:1⟩

… …

r1 (d,f,y,t,s)

r2 (v,b,a,c,d,x)

r3 (s,w,a,g)

r4 (b,z,c,f)

r5 (t,s)June 30, 2011PhD defense

route

trans[] list

r2 ⟨r1,d:5:1⟩,⟨r3,a:3:3⟩,⟨r4,b:2:1⟩,⟨r4,c:4:3⟩

r3 ⟨r1,s:1:5⟩,⟨r2,a:3:3⟩,⟨r5,s:1:2⟩

… …

Traversal paradigms Route traversal paradigm

Traverse collection similar to depth-first search For each route, push all locations after current n in search

stack Access indices on routes to terminate search

RTS: current location and target on same route (R-Index) RTST: current location on route connected to route of target

(T-Index) Link traversal paradigm

Traverse collection similar to depth-first search on links R-Index+ For each route, push first link after current n in search stack

Access indices to create target list T LTS: routes containing target (R-Index+) LTST: routes connected to routes containing target (T-Index) LTS-k: routes connected to routes containing target via first

k links before target (R-Index+)


Traversal paradigms Route traversal paradigm

Traverse collection similar to depth-first search For each route, push all locations after current n in search

stack Access indices on routes to terminate search

RTS: current location and target on same route (R-Index) RTST: current location on route connected to route of target

(T-Index) Link traversal paradigm

Traverse collection similar to depth-first search on links R-Index+ For each route, push first link after current n in search stack

Access indices to create target list T LTS: routes containing target (R-Index+) LTST: routes connected to routes containing target (T-Index) LTS-k: routes connected to routes containing target via first

k links before target (R-Index+)


Traversal paradigms (cont’d)


Expand path (s) Consider every

location after a in routes r1 and r3

Route trav.: PUSH w,a,g

Link trav.: PUSH ar1 (d,f,y,t,s)

r2 (v,b,a,c,d,x)

r3 (s,w,a,g)

r4 (b,z,c,f)

r5 (t,s)



Expand path (s) Consider every

location after a in routes r1 and r3

Route trav.: PUSH w,a,g

Link trav.: PUSH ar1 (d,f,y,t,s)

r2 (v,b,a,c,d,x)

r3 (s,w,a,g)

r4 (b,z,c,f)

r5 (t,s)



RTS, 5th iteration POP d, r1 contains d before

t RTST, 3rd iteration

POP a, r2 connected with r1 containing t via d

LTS, TLTS = {r1, r5}, 4th iteration POP f, r1 contains f before t

LTST, TLTST = {r1,r2,r3,r4,r5}, 2nd iteration POP a, r2 connected with r1

containing t via link d LTS-1, TLTS-1 = {r1,r4,r5}, 3rd

iteration POP c, r2 connected with r1

containing t via link d

r1 (d,f,y,t,s)

r2 (v,b,a,c,d,x)

r3 (s,w,a,g)

r4 (b,z,c,f)

r5 (t,s)











r1 (d,f,y,t,s)

r2 (v,b,a,c,d,x)

r3 (s,w,a,g)

r4 (b,z,c,f)

r5 (t,s)











r1 (d,f,y,t,s)

r2 (v,b,a,c,d,x)

r3 (s,w,a,g)

r4 (b,z,c,f)

r5 (t,s)











r1 (d,f,y,t,s)

r2 (v,b,a,c,d,x)

r3 (s,w,a,g)

r4 (b,z,c,f)

r5 (t,s)











r1 (d,f,y,t,s)

r2 (v,b,a,c,d,x)

r3 (s,w,a,g)

r4 (b,z,c,f)

r5 (t,s)

Index maintenance Indices as inverted files on disk Lazy updates

Buffering phase Update main memory indices

Flushing phase Propagate changes to disk

Insertions Buffering: mark new entries or changed entries in lists Flushing: merge main memory information with disk-

based indices Deletions

No buffering: a list of deleted routes since last flushing Flushing: rebuilding affected lists


Experimental analysis Rival: DFS, depth-first search over links Datasets

Synthetic route collections Vary |R| = {20K, 50K, 100K, 200K, 500K} Vary |Lr| = {3, 5, 10, 30, 50} Vary |N| = {20K, 50K, 100K, 200K, 500K} Vary α = {0.2, 0.4, 0.6, 0.8, 1}

Experiments Index construction Query evaluation (queries with/without answer)

RTS, RTST Vs LTS DFS Vs LTS, LTS-k, LTST

Index maintenance


RTS, RTST Vs LTS

Execution time Execution time


DFS Vs LTS, LTS-k, LTST



Dynamic Pickup and Delivery with Transfers


Solving dPDPT Query

dPDPT(ns,nt) Solution

Modify static plan 4 modifications, called actions, allowed with/without

detours Pickup, delivery, transfer, transport

A sequence of actions, path p Operational cost Op Customer cost Cp

Dynamic plan graph All possible actions

Answer: path p that primarily minimizes Op, secondarily Cp

Algorithms SP and SPMJune 30, 2011PhD defense

Solving dPDPT (cont’d)








If Arrjb < Cp < Depj

b

If Cp < Arrjb

If Cp > Depjb



The SP and SPM algorithms The SP algorithm

Dynamic plan graph violates subpath optimality => path enumeration

Label <Via,p,Op,Cp> for each path to Vi

a

At each iteration select label with lowest combined cost Compute candidate answer – upper bound

Prune search space Terminate search

The SPM algorithm Modified dynamic plan graph

Break Op into Op* and OpR

Subpath optimality Extends SP

Label <Via,p,Op*,OpR> for each path to Vi

a

Most “promising” paths to every vertex


The SP and SPM algorithms The SP algorithm

Dynamic plan graph violates subpath optimality => path enumeration

Label <Via,p,Op,Cp> for each path to Vi

a

At each iteration select label with lowest combined cost Compute candidate answer – upper bound

Prune search space Terminate search

The SPM algorithm Modified dynamic plan graph

Break Op into Op* and OpR

Subpath optimality Extends SP

Label <Via,p,Op*,OpR> for each path to Vi

a

Most “promising” paths to every vertex


The SP and SPM algorithms (cont’d) INITIALIZATION

Pickup Es1a and Es3

b

SP: Q = {<V1a,

(Vs,V1a),6,16>, <V3

b,(Vs,V3

b),6,36>}

SPM: Q = {<V1a,

(Vs,V1a),6,0>, <V3

b,(Vs,V3

b),6,0>}

pcand = null

T = 6


The SP and SPM algorithms (cont’d) POP <V1

a, (Vs,V1a),…,

…> Transport E12

a

SP: Q = {<V2a,

(Vs,V1a,V2

a),6,26>, <V3

b,(Vs,V3b),6,36>}

SPM: Q = {<V2a,

(Vs,V1a,V2

a),6,0>, <V3

b,(Vs,V3b),6,0>}

pcand = nullT = 6



a, (Vs, V1a,V2

a),…,…> Transfer E25

ac

Arr5c = 10 < 26 <

Dep5c = 40

SP: Q = {<V3b,

(Vs,V3b),6,36>, <V5

c, (Vs,V1

a,V2a,V5

c),18,36>} SPM: Q = {<V3

b,(Vs,V3

b),6,0>, <V5c,

(Vs,V1a,V2

a,V5c),6,12>}

pcand = nullT = 6



b, (Vs,V3b),6,36>

and <V4b, (Vs,V3

b,V4b),6,46>

Transport E34b and transfer

E46bc

46 > Dep6c = 40

SP: Q = {<V5c,

(Vs,V1a,V2

a,V5c),18,36>,

<V6c,

(Vs,V3b,V4

b,V6c),24,52>}

SPM: Q = {<V5c,

(Vs,V1a,V2

a,V5c),6,12>, <V6

c,(Vs,V3

b,V4b,V6

c),12,12>}

pcand = nullT = 6



c,(Vs,V1

a,V2a,V5

c),…,…> Transport E56

c

SP: Q = {<V6c,

(Vs,V1a,V2

a,V5c,V6

c),18, 46>, <V6

c,(Vs,V3

b,V4b,V6

c),24,52>} SPM: Q = {<V6

c,(Vs,V1

a,V2a,V5

c,V6c),6,

12>, <V6c,

(Vs,V3b,V4

b,V6c),12,12>}

pcand = nullT = 6



c,(Vs,V1

a,V2a,V5


c

SP: Q = {<V6c,

(Vs,V1a,V2

a,V5c,V6

c),18, 46>, <V6

c,(Vs,V3

b,V4b,V6

c),24,52>} SPM: Q = {<V6

c,(Vs,V1

a,V2a,V5

c,V6c),6,

12>, <V6c,

(Vs,V3b,V4

b,V6c),12,12>}

pcand = nullT = 6



c,(Vs,V1

a,V2a,V5


c

SP: Q = {<V6c,

(Vs,V1a,V2

a,V5c,V6

c),18, 46>, <V6

c,(Vs,V3

b,V4b,V6

c),24,52>}

SPM: Q = {<V6c,

(Vs,V1a,V2

a,V5c,V6

c),6, 12>}

pcand = nullT = 6



c,(Vs,V1

a,V2a,V5

c,V6c),…,…>

Transport E67c

SP: Q = {<V7c,

(Vs,V1a,V2

a,V5c,V6

c,V7c),

18, 56>, <V6c,

(Vs,V3b,V4

b,V6c),24,52>}

SPM: Q = {<V7c,

(Vs,V1a,V2

a,V5c,V6

c,V7c),

6,12>} pcand = null

T = 6



c,(Vs,V1

a,V2a,V5

c,V6c,V7

c), …,…> Delivery E7e

c

FOUND pcand

SP: Q = {<V6c,

(Vs,V3b,V4

b,V6c),24,52>}

SPM: Q = {} END pcand =

(Vs,V1a,V2

a,V5c,V6

c,V7c)

Opcand = 24

Cpcand = 59T = 6



c,(Vs,V3

b,V4b,V6

c),24,52>

Opcand = 24 SP: END

T = 6


Experimental analysis Rival: two-phase method, HTT

Cheapest insertion for pickup and delivery location, for every new request

After k requests perform tabu search Datasets

Road networks, OL with 6105 locations, ATH with 22601 locations

Static plan with HTT method Vary |Reqs| = {200, 500, 1000, 2000} Vary |R| = {100, 250, 500, 750, 1000}

Stored on disk Experiments

500 dPDPT requests HTT1, HTT3, HTT5

Measure Total operational cost increase Total execution time


Vary |Reqs|

Operational cost increase Execution time

OL road network


Vary |R|

Operational cost increase Execution time

OL road network


Most Trusted Near Shortest Path


Identifying MTNSP Query

MTNSP(ns,nt,α) Solution

Known graph Unknown graph Two costs for a path p

Unknown time Up Length Lp

Answer: path p with lowest unknown time Up and length Lp ≤ α dN(ns,nt)

Offline processing phase Lipschitz Embedding

Online processing phase The TRUSTME algorithm


The known and unknown graphs


Known subgraph Unknown subgraph

Network graph

Offline processing phase Embedding

For each node n in network graph, precompute shortest paths to every node nk in known graph

Store dN(n,nk)

Uk lowest unknown time

Compute bounds d≥

N(ns,nt), d≤N(ns,nt)

U≥p, U≤p for p(ns,…,nt)

dN ns n1 n5 n6 n7

ns 0 3 9 11 18

n1 3 0 6 8 15

n2 8 5 2 3 10

… … … … … …

nt 20 17 14 11 4


Up ns n1 n5 n6 n7

ns 0 0 0 8 8

n1 0 0 0 8 8

n2 5 5 2 3 3

… … … … … …

nt 17 17 14 4 4



Store dN(n,nk)


Compute bounds d≥



dN ns n1 n5 n6 n7

ns 0 3 9 11 18

n1 3 0 6 8 15

n2 8 5 2 3 10

… … … … … …

nt 20 17 14 11 4


Up ns n1 n5 n6 n7

ns 0 0 0 8 8

n1 0 0 0 8 8

n2 5 5 2 3 3

… … … … … …

nt 17 17 14 4 4



Store dN(n,nk)


Compute bounds d≥



12 ≤ dN(n2,nt) ≤ 14

dN ns n1 n5 n6 n7

ns 0 3 9 11 18

n1 3 0 6 8 15

n2 8 5 2 3 10

… … … … … …

nt 20 17 14 11 4


Up ns n1 n5 n6 n7

ns 0 0 0 8 8

n1 0 0 0 8 8

n2 5 5 2 3 3

… … … … … …

nt 17 17 14 4 4

Online processing phase The TRUSTME algorithm

Label-setting Label <n,p,Up,Lp> for each path to n Only the labels of most “promising” paths to every node n

At each iteration select label with lowest Lp Compute an upper bound of the unknown time of

the answer Prune search space Terminate search

Expansion: Exploit d≤

N, d≥N, U≤p,U≥p to prune search space


Online processing phase (cont’d)


INITITALIZATION Q = {<ns, (ns), 0, 0} L = d≤

N(ns,nt) = 20 U = null pcand = null

α = 1.3



POP <n1, (ns,n1), 3, 0> Edges (n1,ns), (n1,n2),

(n1,n5) Edge (n1,n6)

p(ns,n1,n6), Lp = 17 Lp + d≥

N(n6,nt) = 17 + 11 = 28 > α L = 26

Discard p L = d≤

N(ns,nt) = 20 U = null pcand = nullα = 1.3



POP <n7, p(ns,n1,n2,n6,n7), 18,8> Lp = 18 < dN(ns,nt) Lp + dN(n7,nt) = 22 <

1.3 Lp = 23.4 FOUND upper bound

for the unknown time of answer

L = d≤N(ns,nt) = 20

U = 12 pcand = nullα = 1.3



POP <nt, p(ns,n1,n2,n3,n4,nt),20,17> Up > U = 12 Not an answer L = d≤

N(ns,nt) = 20 U = 12 pcand = null

α = 1.3



POP <nt, p(ns,n1,n5,n2,n6,n7,n4,nt),25,9> Q = {} END pcand =

(ns,n1,n5,n2,n6,n7,n4,nt) Lpcand = 25 Upcand = 9

α = 1.3

Experimental analysis Rival: label setting SP-EUCLIDEAN First computing shortest path Considering euclidean distance as lower bound Datasets Road networks, OL with 6105 locations, TG with 18263

locations Familiar neighborhoods Vary |H| = {3, 4, ,5, 10, 30} Vary α = {1.1, 1.2, 1.3, 1.4, 1.5} Three strategies for creating known subgraph

S1: all locations in neighborhoods S2: all locations on shortest path between neighborhoods

centers S3: combination

Stored on diskJune 30, 2011PhD defense

Strategy S1



Strategy S2



Conclusions Framework for evaluating path queries on

frequently updated route collections Indexing schemes Evaluation algorithms

Three query cases PATH query on large disk-resident collections dynamic Pickup and Delivery with Transfers Most Trusted Near Shortest Path


Future work Trip planning or optimal sequence like queries

Find a path passing through a Museum, then a Stadium and finally a Restaurant

Combine query evaluation with keyword search Find a path passing through a Restaurant relevant to

“sea food, lobster” Adopt ideas from PATH query for dPDPT

Exploit R-Index/T-Index to identify a candidate answer sooner

Additional constraints for dPDPT Vehicle capacity, time windows

Handle updates on embedding scheme for MTNSP Inverted index on precompute shortest paths

Complexity analysis for dPDPT and MTNSPJune 30, 2011PhD defense

Publications PATH

Evaluating Path Queries over Frequently Updated Route Collections, TKDE’11

Evaluating Path Queries over Route Collections, ICDE’10-PhD Evaluating Reachability Queries Over Path Collections,

SSDBM’09 Evaluating "Find a Path" Reachability Queries, ECAI’08-

STRWS dPDPT

Efficient Dynamic Pickup and Delivery with Transfers, TR KDBSL

Dynamic Pickup and Delivery with Transfers, SSTD’11 MTNSP

Most Trusted Near-Shortest Path, TR KDBSL


Other works Set-values

Efficient Answering of Set Containment Queries for Skewed Item Distributions, EDBT’11

Skyline queries Caching Dynamic Skyline Queries, SSDBM’08

Managing and personalizing topic directories Mining User Navigation Patterns for

Personalizing Topic Directories, CIKM’07-WIDM PatMan: A Visual Database System to

Manipulate Path Patterns and Data in Hierarhical Catalogs, AVIVDiLib’05

PatManQL: A language to manipulate patterns and data in hierarchical catalogs, EDBT’04-PaRMa


Thank you!


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Evaluating Queries over Route Collections Panagiotis Bouros, PhD defense.

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