Multi-Approximate-Keyword Routing Query - University of Utah ...

Multi-Approximate-Keyword Routing Query

Bin Yao1, Mingwang Tang2, Feifei Li2

1Department of Computer Science and Engineering 2School of ComputingShanghai Jiao Tong University, P. R. China University of Utah, USA

Outline

1 Introduction and Motivation

2 Preliminary

3 Exact solutions

4 Approximate solutions

5 Experiments

6 Related Work and Concluding Remarks

Bin Yao, Mingwang Tang, Feifei Li Multi-Approximate-Keyword Routing Query

Introduction and motivation

Approximate keyword search is important:

GIS data has errors and uncertainty with it.GIS data is keeping evolving, routinely data cleaning and dataintegration is expensivePeople may make mistakes in query input (typos)

Shortest path search has many applications:

map service.strategic planning of resources

Our work: Multi-Approximate-Keyword Routing (MAKR) query.

A combination of shortest path search and approximate keywordsearchGiven a source and destination pair (s, t) and a query keyword set ψon a road network, the goal is to find the shortest path that passesthrough at least one matching object per keyword.


















Multi-Approximate-Keyword Routing (MAKR) query

Vertex

Point

Edge

t

s

p9: theater

p7: theatre

p2: Bob’s market

p10: Spielberg

p6: Spielburg

p4: Moe’s Club

p8: grocery

p1: gymp5: Museum

v1

v2

v3v4

v5 v6

v7v8

p3: theate



Vertex

Point

Edge

t

s

p9: theater

p7: theatre

p2: Bob’s market

p10: Spielberg

p6: Spielburg

p4: Moe’s Club

p8: grocery

p1: gymp5: Museum

v1

v2

v3v4

v5 v6

v7v8

p3: theate

Approximate string similarity:edit distance ε(δ1, δ2) = τ .



Vertex

Point

Edge

t

s

p9: theater

p7: theatre

p2: Bob’s market

p10: Spielberg

p6: Spielburg

p4: Moe’s Club

p8: grocery

p1: gymp5: Museum

v1

v2

v3v4

v5 v6

v7v8

p3: theate

Example: s, t, ψ = {(δ1 = theater, τ1 = 2), (δ2 = Spielberg, τ2 = 1)}.



Vertex

Point

Edge

t

s

p9: theater

p7: theatre

p2: Bob’s market

p10: Spielberg

p6: Spielburg

p4: Moe’s Club

p8: grocery

p1: gymp5: Museum

v1

v2

v3v4

v5 v6

v7v8

c1

p3: theate

Example: s, t, ψ = {(δ1 = theater, τ1 = 2), (δ2 = Spielberg, τ2 = 1)}.ε(δ1, p7.δ) = 2 ε(δ2, p10.δ) = 0



Vertex

Point

Edge

t

s

p9: theater

p7: theatre

p2: Bob’s market

p10: Spielberg

p6: Spielburg

p4: Moe’s Club

p8: grocery

p1: gymp5: Museum

v1

v2

v3v4

v5 v6

v7v8

c2

p3: theate


path length: d(c2) < d(c1)

ε(δ1, p9.δ) = 0 ε(δ2, p6.δ) = 1



Vertex

Point

Edge

t

s

p9: theater

p7: theatre

p2: Bob’s market

p10: Spielberg

p6: Spielburg

p4: Moe’s Club

p8: grocery

p1: gymp5: Museum

v1

v2

v3v4

v5 v6

v7v8

p3: theate


ψ(c) = {δ1 = theater}

c : candidate path



Vertex

Point

Edge

t

s

p9: theater

p7: theatre

p2: Bob’s market

p10: Spielberg

p6: Spielburg

p4: Moe’s Club

p8: grocery

p1: gymp5: Museum

v1

v2

v3v4

v5 v6

v7v8

p3: theate


ψ(c) = {δ1 = theater}|ψ| = κ, when ψ(c) = ψ, c becomes a qualified path

c : candidate path


Outline


2 Preliminary

3 Exact solutions


5 Experiments



Data structure: Disk-based storage of the road network

v1

v2

v3 v4

v5 v6

v7v8

d(v1, v2) = 6d(v1, v8) = 8

gym

Bob’s market

theate

p1

p2

p3

d(v1, p1) = 1d(v1, p2) = 3d(v1, p3) = 5

vi : network vertex.

RDISTi : distances to the landmarks.

[sl97]: CCAM: A connectivity-clustered access method for networks andnetwork computations. In IEEE TKDE, 1997.

[gh05]: Computing the shortest path: A∗ search meets graph theory. In

SODA, 2005.



v1

v2

v3 v4

v5 v6

v7v8

d(v1, v2) = 6d(v1, v8) = 8

gym

Bob’s market

theate

p1

p2

p3

d(v1, p1) = 1d(v1, p2) = 3d(v1, p3) = 5

v1, Rdist1, 2v2 6

v8 8

v2, Rdist2, 3v1

v3

v5

· · ·...

Adjacencylist B+-tree

...

1

2

3

Adjacency list file

6

2

8

vi : network vertex.RDISTi : distances to the landmarks.



SODA, 2005.



v1, Rdist1, 2v2 6

v8 8

v2, Rdist2, 3v1

v3

v5

· · ·...

(v1, v2), 3

13

gym

Bob’s market

(v1, v8), 2

3

· · ·...


...

1

2

3

Points fileB+-tree

...

1

4

6

Adjacency list file Points file

6

2

8 6

Moe’s Club

12

4

5

3 5 theate

Museum

v1

v2

v3 v4

v5 v6

v7v8

d(v1, v2) = 6d(v1, v8) = 8

gym

Bob’s market

theate

p1

p2

p3

d(v1, p1) = 1d(v1, p2) = 3d(v1, p3) = 5




SODA, 2005.



v1, Rdist1, 2v2 6

v8 8

v2, Rdist2, 3v1

v3

v5

· · ·...

(v1, v2), 3

13

gym

Bob’s market

(v1, v8), 2

3

· · ·...


...

1

2

3

Points fileB+-tree

...

1

4

6

Adjacency list file Points file

6

2

8 6

Moe’s Club

12

4

5

3 5 theate

Museum

v1

v2

v3 v4

v5 v6

v7v8

d(v1, v2) = 6d(v1, v8) = 8

gym

Bob’s market

theate

p1

p2

p3

d(v1, p1) = 1d(v1, p2) = 3d(v1, p3) = 5




SODA, 2005.


Data structure: FilterTree for ApproximateKeywords-Matching

· · ·aa

jozz

13

n

Prefix filter

Position filter· · ·

· · ·· · ·

1 2

An inverted list (point ids whoseassociated strings have length of 3and the gram ”jo” at position 2)

4719...

· · ·root

Length filter

[lll08]: Efficient merging and filtering algorithms for approximate string

searches. In ICDE, 2008.Bin Yao, Mingwang Tang, Feifei Li Multi-Approximate-Keyword Routing Query

Outline


2 Preliminary

3 Exact solutions


5 Experiments



Exact solution overview

Intuition: PER–Path Expansion and Refinement.




Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}For each keyword w ∈ ψ − ψ(c), add a point p from

P(w) into current shortest candidate path, s.t. ∀p ∈P(w), ε(p.δ,w) ≤ τw , to minimize the impact to d(c)




Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}

s tp1 : ee

p2 : ch

p3 : yb

For each keyword w ∈ ψ − ψ(c), add a point p from


p4 : zb

{s, p1, t}

{s, p3, t}{s, p2, t}

IO efficient priority queue of

candidate paths: initialized

with c ’s tha each covers a din-

stinct, single w ∈ ψ

L




Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}

s tp1 : ee

p2 : ch

p3 : yb



p4 : zb

ψ(c) = {ef }ψ−ψ(c) = {ab, cd}




Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}

s tp1 : ee

p2 : ch

p3 : yb



p4 : zb

ψ(c) = {ef }ψ−ψ(c) = {ab, cd}

insert sp1p3t to L




Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}

s tp1 : ee

p2 : ch

p3 : yb



p4 : zb

ψ(c) = {ef }ψ−ψ(c) = {ab, cd}

insert sp1p2t to L



Improvement.

use Landmarks to estimate distances when finding points;modify and then combine with FilterTree to find p ∈ P(w)incrementally;refine d(c) when c becomes a qualified path.

two methods to refine d(c): PER-full and PER-partial


Outline


2 Preliminary

3 Exact solutions


5 Experiments



Approximate solutions for MAKR query

Problem with the exact solution:Theorem 1: The MAKR problem is NP-hard.

Approximate solutions:

The local minimum path algorithms: ALMP1 and ALMP2.The global minimum path algorithm: AGMP .


Approximate solutions for MAKR query

Problem with the exact solution:Theorem 1: The MAKR problem is NP-hard.

Approximate solutions:

The local minimum path algorithms: ALMP1 and ALMP2.The global minimum path algorithm: AGMP .


The local minimum distance algorithms: ALMP1 and ALMP2

s t

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}



s tp1 : ee

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}For each segment (pi , pj), find a point p, p.δ similar to keywords

in ψ − ψ(c), to minimize sum of d(pi , p) and d(p, pj).



s tp1 : ee

p2 : ch





s tp1 : ee

p2 : ch

p3 : yb





s t

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}



s t

For each keyword w ∈ ψ − ψ(c), we iterate through

the segments in c and add the point p ∈ P(w), which

minimizes d(c), to one segment (pi , pj) of c .

p1 : yb

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}



s t




p1 : yb

p2 : ch

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}



s t




p1 : yb

p2 : ch

p3 : ee

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}


The minimum distance algorithm: AGMP

s t

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}

Theorem 2: The AGMP algorithm gives a κ-approximate path. Thisbound is tight.



s t

p1 : yb

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}For each keyword w ∈ ψ − ψ(c), finda point p ∈ P(w) to minimize sum ofd(s, p) and d(p, t).




s t

p1 : yb

p2 : ee

p3 : ch

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}For each keyword w ∈ ψ − ψ(c), finda point p ∈ P(w) to minimize sum ofd(s, p) and d(p, t).




s tp2 : ee

p3 : ch

p1 : yb

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}




s tp2 : ee

p3 : ch

p1 : yb

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}




s tp2 : ee

p3 : ch

p1 : yb

Q : s, t, ψ = {(ab, 1), (cd , 1), (ef , 1)}



Challenges in approximate solutions

Challenges in all approximate methods:

how to find p ∈ P(w) incrementally for each type of objectivefunction (instead of finding P(w) all at once and iterate throughpoints in P(w) one by one)?how to avoid exact distance computation as much as possible?


Improvement on approximate solutions by networkpartitioning

Voronoi-diagram-like partition (by Erwig and Hagen’s algorithm).

: Vetex

d−(p,Gi ): lower bound distance from p to the boundary of Gi , computedusing the landmarks.

d−(s,Gi ) + d−(Gi , t) ≤ d−(s, p) + d−(p, t),∀p ∈ Gi .




G1G2

G3

: Vetex






: Vetex






: Vetex






G1G2

G3

: Vetex






G1G2

G3

: Vetex




Extensions

Top-k MAKR query:

Exact methods.Approximate methods.

Multiple strings.

Updates.


Extensions

Top-k MAKR query:


Multiple strings.

Updates.


Extensions

Top-k MAKR query:


Multiple strings.

Updates.


Outline


2 Preliminary

3 Exact solutions


5 Experiments



Experiment setup

All experiments were executed on a Linux machine with an IntelXeon CPU at 2.13GHz and 6GB of memory.

Data sets:

road networks from the Digital Chart of the World Server:City of Oldenburg (OL,6105 vertices, 7029 edges)California(CA,21048 vertices, 21693 edges)North America (NA,175813 vertices, 179179 edges)building locations in OL, CA and NA from the OpenStreetMapproject.

The default experimental parameters:Symbol Definition Default Value|P| number of points for exact solution 10, 000|P| number of points for approximate solution 1, 000, 000κ number of query strings 6τ edit distance threshold 2

road network CA


Experiment setup


Data sets:



road network CA


Experiment setup


Data sets:



road network CA


Query time:

2 4 6 8 1010

−2

10−1

100

101

102

103

κ

Run

ning

Tim

e (s

ecs)

PER−partial PER−full

AGMP

ALMP1

ALMP2

|P| = 10, 000


Query time:

103

104

105

10610

−1

100

101

102

103

|P|

Run

ning

Tim

e (s

ecs)


AGMP

ALMP1

ALMP2

|P| = 10, 000


Query time:

10−2

10−1

100

101

102

103

Run

ning

Tim

e (s

ecs)

OL CA NA

PER−partialPER−fullA

GMPA

LMP1A

LMP2

|P| = 10, 000


Query time:

1 2 310

−1

100

101

102

103

τ

Run

ning

Tim

e (s

ecs)


AGMP

ALMP1

ALMP2

|P| = 10, 000


Scalability of approximate solutions:

2 4 6 8 100

3

6

9

12

15

κ

Run

ning

Tim

e (s

ecs)

AGMP

ALMP1

ALMP2

|P| = 1, 000, 000



0.5 1 1.5 20

2

4

6

8

|P|: X106

Run

ning

Tim

e (s

ecs)

AGMP

ALMP1

ALMP2

|P| = 1, 000, 000



10−1

100

101

102

Run

ning

Tim

e (s

ecs)

OL CA NA

AGMP

ALMP1

ALMP2

|P| = 1, 000, 000



1 2 30

3

6

9

12

15

τ

Run

ning

Tim

e (s

ecs)

AGMP

ALMP1

ALMP2

|P| = 1, 000, 000


Approximation quality:

2 4 6 8 10

1

1.5

2

2.5

κ

r: A

ppro

xim

atio

n R

atio

AGMP

ALMP1

ALMP2



103

104

105

106

1

1.5

2

2.5

|P|

r: A

ppro

xim

atio

n R

atio

AGMP

ALMP1

ALMP2



1

1.3

1.6

1.9

2.2

r: A

ppro

xim

atio

n R

atio

OL CA NA

AGMP

ALMP1

ALMP2



1 2 3

1

1.5

2

2.5

τ

r: A

ppro

xim

atio

n R

atio

AGMP

ALMP1

ALMP2


Outline


2 Preliminary

3 Exact solutions


5 Experiments



Related work

The optimal sequenced route (OSR) query [sks07].

Exact keyword query and only handles the query keywordssequentially.

In MAKR queries, “categories” are dynamically decided only at thequery time.

: different keywords.

[sks07]: The Optimal Sequenced Route Query. In VLDBJ, 2007.


Related work




Q = s, t, ( )

s

t: different keywords.



Related work




Q = s, t, ( )

s


c



Related work




Q = s, t, ( )

s


c



Related work




Q = s, t, ( )

s


c



The end

Thank You

Q and A


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