1. Efficient Evaluation of k-NN Queries Using Spatial Mashups
Detian Zhang1, 2, Chi-Yin Chow1, Qing Li1
Xinming Zhang2, and Yinlong Xu2
1City University of Hong Kong
2University of Science and Technology of China

2. SSTD 2011
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Introduction (1/3)
The k-nearest-neighbor (k-NN) query is one of the most important location-based services
E.g., store finder – find the 10 nearest restaurants
Most existing k-NN queries measure distance between a query and an object by “Euclidean” distance or “network” distance
In reality, the shortest path may not be the one with the shortest travel time

3. Where is my nearest clinic?
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Introduction (2/3)
Distance: 500 meters
Travel time: 10 mins
Where is my nearest clinic?
Distance: 1000 meters
Travel time: 3 mins
Travel time is more meaningful for LBS!!!

4. Real-world travel time for a weekday on a segment of I-405 in LA, USA
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Introduction (3/3)
Since the travel time is highly dynamic, we cannot accurately predict it based on the network distance
Real-world travel time for a weekday on a segment of I-405 in LA, USA
Source: U. Demiryurek, F. Banaei-Kashani and C. Shahabi, “Efficient K-Nearest Neighbor Search in Time-Dependent Spatial Networks”, DEXA 2010.

5. Web Mapping Services (1/2)
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Web Mapping Services (1/2)
Solutions for traffic monitoring
Collect GPS data from vehicles
Deploy road-side sensors ……
They are good but too expensive!!!
Why not ask Web mapping services (e.g., Google Maps, Yahoo! Maps, and Microsoft Bing Maps) for help?
Provide direction and travel time between two locations
Server-side spatial mashups
[Wikipedia: A client-side mashup is a Web page or application that uses and combines data, presentation or functionality from multiple sources to create new services.]

6. Web Mapping Services (2/2)
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Web Mapping Services (2/2)
Google Directions API provides more turn-by-turn direction information

7. Limitations of Spatial Mashups (1/2)
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Limitations of Spatial Mashups (1/2)
Expensive external requests
E.g., retrieving travel time from the Microsoft MapPoint Web service by a database takes 502ms while the time needed to read a cold and hot 8KB buffer page from disk is 27ms and ms, respectively [Source: J. J. Levandoski, M. F. Mokbel, and M. E. Khalefa. “Preference Query Evaluation Over Expensive Attributes”, ACM CIKM 2010.]
Limit on the number of requests
E.g., Google Maps allows only 2,500 requests per day for evaluation users and 100,000 requests per day for premier users

8. Limitations of Spatial Mashups (2/2)
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Limitations of Spatial Mashups (2/2)
Only support primitive operations
E.g., the direction and travel time information between two point locations
Restrictions on retrieved direction information
E.g., The direction information must not be pre-fetched, cached, or stored, except only limited amount of content can be temporarily stored for the purpose of improving system performance [Source: Google Maps APIs Terms of Service]

9. Problem Definition Given a set of spatial objects and a query with
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Problem Definition
Given a set of spatial objects and a query with
A user’s location ()
A user-specified maximum number of returned objects (k)
A user-specified maximum travel time (tmax)
Find
At most k nearest objects of interest to  in terms of travel time through accessing a Web Mapping Service
The travel time from  to each returned object ≤ tmax
Objectives
Minimize the number of external requests
Maximize the accuracy of query answers

10. Web Mapping Service Provider
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System Model (1/2)
External Data
(e.g., direction information)
Queries
(High Cost)
Database Server
Web Mapping Service Provider
Mobile User
(Low Cost)
Local Data
(e.g., restaurant data)

11. System Model (2/2) (a) A road map (b) A graph model I1 I2 I10 I9 I6 I5
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System Model (2/2)
(a) A road map
(b) A graph model I1 I2
I10 I9 I6 I5 I7 I8 I4 I3
I11
I12
I13
I15
I14
Road segment
Intersection

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A Basic Algorithm
Find a set of candidate objects R by executing a range query from the user U to the maximum possible travel distance dmax
dmax = U’s specified maximum travel time (tmax) X the maximum allowed travel speed
Issue one external request for each object in R to compute a query answer I1 I2 I3 I4 R4 R6 R5 I7 R7 I8 R8 I5 I6 R3 U R9 R2 I9 R1
I10
I11
R10
I12
I13
I14
I15
User
Object
Intersection

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Can We Do Better?
We observe that many spatial objects are generally located in clusters in reality.
E.g., many restaurants are located in a shopping area, around a university, and around a commercial center.
Object grouping
Group nearby spatial objects to a representative point location P
Issue an external request from a user to P
Share the retrieved direction information among the objects in the group by estimating the travel time from P to them

14. Object Grouping Q1: How to select representative point locations?
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Object Grouping
Q1: How to select representative point locations?
S: All Intersections.
Only one possible path from the intersection of a group to each object in the group => make the estimation easier and more accurate
A road segment should have the same conditions, e.g., speed limit and direction => considering a road segment as a basic unit makes the estimation more accurate and nature
Q2: How to group objects to representative locations?
S: (1) minimize the distance from objects to their representative location and (2) minimize the number of shared intersections

15. An Efficient Algorithm
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An Efficient Algorithm
Step 1: Range Search
Find a set of candidate objects R
Step 2: Object Grouping
Group each object in R to its nearest intersection
Step 3: External Requests
Issue one external request for each shared intersection in increasing order of its network distance to U
For each shared intersection, its direction information is shared by the objects in its group
Step 4: Object Pruning
Maintain the largest travel time Amax in a current answer
If an object R in R has the smallest possible travel time not less than Amax, R is pruned.
dist(I6,I5)=30
time(I6,I5)=20 I1 I2 I3 I4 R4
dist(U,I6)=5
time(U,I6)=10 R6 R5
dist(I5,R2)=20
time(I5,R2)=10 I7 R7 I8 R8 I5 I6 R3 U R9 R2 I9 R1
I10
I11
R10
I12
dist(I5,I9)=30
time(I5,I9)=15
I13
I14
I15
User
Object
Intersection

16. Minimize the No. of Shared Intersections
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Minimize the No. of Shared Intersections
Problem: Find a minimal set of intersections that cover all road segments having candidate objects
The same as vertex cover problem
Use a greedy approach to find an approximate solution

17. The Greedy Approach Selection of shared intersections I1 I2 I3 I4 d=1
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The Greedy Approach
Selection of shared intersections I1 I2 I3 I4
d=1
d=0 R4 I2
Degree (d): the number of edges connected to the vertex R5 I7 I8 R8
d=1
d=0
d=1 I5 I6
d=0
d=1 U I5 I6 R9 I7 R2
d=2
d=0
d=1
d=2
d=0
d=1 I9 R1
I10
I11
R10
I12 I9
I10
I11
I12
The minimal intersection set V={I11, I9 , I6}
The minimal intersection set V={I11, I9}
The minimal intersection set V={I11}
I13
I14
I15
User
Object
Intersection

18. Extensions Support one-way roads User grouping
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Extensions
Support one-way roads
Only need to slightly modify the objects grouping methods
User grouping
Effective for continuous queries or a system with a high workload
First, execute user grouping step (new) – group users to their nearest intersection based on their movement direction
Then, execute our algorithm with modifications in the range search and object pruning steps

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Experiment Settings
Implement our algorithms using Google Direction APIs
Road map: An area of 88 km2 in Hennepin County, MN, USA
6,109 road segments and 3,593 intersections
Two object grouping methods
NI – minimize the distance from objects to representative locations
MI – minimize the number of shared intersections
Parameter settings
100 users and 500 objects
Maximum allowed travel speed is 110 km per hour
User-specified maximum travel time (tmax) is 120 seconds

20. Experiment Results (1/2)
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Experiment Results (1/2)
Accuracy of the travel time estimation

21. Experiment Results (2/2)
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Experiment Results (2/2)
Accuracy of k-NN query answers

22. Simulation Settings Implement our algorithms using Google Maps APIs
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Simulation Settings
Implement our algorithms using Google Maps APIs
Road map: An area of 88 km2 in Hennepin County, MN, USA
6,109 road segments and 3,593 intersections
Two objects grouping methods
NI – minimize the distance from objects to representative points
MI – minimize the number of shared intersections
Parameter settings
10,000 users and 10,000 objects
Maximum allowed travel speed is 110 km per hour
User specified maximum travel time (tmax) is 120 seconds
User specified number of returned objects (k) is 20

23. Simulation Results Effect of the number of objects from 4K to 20K
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Simulation Results
Effect of the number of objects from 4K to 20K
No. of External Requests
Query Response Time (s)

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Conclusion
Efficient Evaluation of k-NN Queries Using Spatial Mashups
Spatial
Databases
k-Nearest-
Neighbor Queries
Web Mapping
Services ?

25. Simulation Results Effect of the number of users from 4K to 20K
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Simulation Results
Effect of the number of users from 4K to 20K

26. SSTD 2011
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Simulation Results
Effect of the user required maximum travel time (tmax)