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Optimized Graph Search Using Multi-Level Graph Clustering. Rahul Kala, Department of Information Technology Indian Institute of Information Technology and Management Gwalior http://students.iiitm.ac.in/~ipg_200545/ rahulkalaiiitm@yahoo.co.in, rkala@students.iiitm.ac.in.

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optimized graph search using multi level graph clustering

Optimized Graph Search Using Multi-Level Graph Clustering

Rahul Kala,

Department of Information Technology

Indian Institute of Information Technology and Management Gwalior

http://students.iiitm.ac.in/~ipg_200545/

rahulkalaiiitm@yahoo.co.in,

rkala@students.iiitm.ac.in

Kala, Rahul, Shukla, Anupam & Tiwari, Ritu (2009) Optimized Graph Search using Multi Level Graph Clustering, Proceedings of the Springer International Conference on Contemporary Computing, IC3'09, pp 103-114, Noida, India

slide2

Multi Neuron Heuristic Search

Breadth First Search

Iterative Deepening Search

Graph Searching Algorithms

Depth First Search

A* Algorithm

Heuristic Search Algorithm

clustering algorithm
Clustering Algorithm

g ← original graph

for i = 1 to A

g ← makeCluster(g)

Is there change in g

Add g to graphs

Yes

No

break

making clusters

9

5

10

Making Clusters

1

2

5

6

3

4

7

8

making clusters algorithm
Making Clusters Algorithm

Make Clusters()

Step1: While more clusters are possible

Step2: c ← getNextCluster()

Step3: for each vertex v in c

Step4: Delete v from graph and delete all edges from/to it

Step5: Add a new unique vertex v2

Step6: Add edges from/to v2 that were deleted from the graph

Step7: Add information of cluster v2 to set of clusters in the particular level

star vertex
Star Vertex

Star Vertex

selecting nodes of cluster
Selecting Nodes of Cluster

getNextCluster()

Step1: Find the vertex v in graph with maximum edges

Step2: If the maximum edges are less than α then return null

Step3: c ← all vertices that are at a maximum distance of 2 units away from v

Step4: Sort c in order of decreasing number of edges of vertices

Step5: Select any 3 vertices v1, v2, v3 in c such that all 3 vertices are connected to β common vertices

Step6: c2 ← all vertices in c that are connected to v1 and v2 and v3

Step7: Add all vertices in c to c2 that are connected to at least 4 vertices already present in c2

Step8: Return c2

point search
Point Search

Source

Source

Goal

Goal

Goal

Source

Source and Goal

point algorithm

Level ← 0

Is source member of any cluster of this level

While there are graphs in current level

Yes

Source ← Cluster number where it was found

No

Is goal member of any cluster of this level

Goal ← Cluster number where it was found

Yes

No

Add source, destination to point set

Level ← Level + 1

Point Algorithm
search algorithm
Search Algorithm

Source

Source

Goal

Goal

Goal

Source

Source and Goal

search algorithm1
Search Algorithm

Search()

Step1: Solution ← null

Step2: For each (source, destination) in point set

Step3: Solution2 ← start + all vertices in solution + destination

Step4: If any vertex in solution2 is a cluster of the higher level

Step5: Replace that vertex with the star vertex of that cluster

Step6: Solution ← null

Step7: For all adjacent vertices (v1,v2) in Solution2, taken in order

Step8: Solution ← Solution + bfs(current level graph,v1,v2) – v2

Step9: Solution ← Solution + destination

future scope
Future Scope
  • Validation against actual data
  • Weighted Graphs
  • Clustering Criterion
  • Tradeoff between loss of result quality with time
  • Type of graphs
references
References

1. Anders Karl-Heinrich, ‘A Hierarchical Graph-Clustering Approach to find Groups of Objects’, In ICA Commission on Map Generalization, 5th Workshop on Progress in Automated Map Generalization (2003)

2. Arcaute Esteban, Chen Ning, Kumar Ravi, Liben-Nowell David, Mahdian Mohammad, Nazerzadeh Hamid, Xu Ying, ‘Deterministic Decentralized Search in Random Graphs’, Proceedings of the 5th Workshop on Algorithms and Models for the Web-Graph, (2007)

3. Brandes Ulrik, Gaertler Marco, Wagner Dorothea, ‘Experiments on Graph Clustering Algorithms’, In Proceedings of the 11th Annual European Symposium on Algorithms. Lecture Notes in Computer Science, vol. 2832. 568--579 (2003)

4. Craswell Nick, Szummer Martin, ‘Random Walks on the Click Graph’, SIGIR Conf Research and Development in Information Retrieval, 239—246 (2007)

5. Goldberg Andrew V., Harrelson Chris, ‘Computing the Shortest Path: A* Search Meets Graph Theory’, In Proceedings of SODA, 156—165 (2005)

6. Gunter Simon, Bunke Horst, ‘Validation indices for graph clustering’, Pattern Recognition Letters 24, 1107--1113 (2003)

7. He Hao, Wang Haixun, Yang Jun, Yu Philip S,’ BLINKS: Ranked Keyword Searches on Graphs’, in the ACM International Conference on Management of Data (SIGMOD), Beijing, China.(2007)

slide28

8. Hlaoui Adel, Wang Shengrui, ‘A Graph Clustering Algorithm with Applications to Content-Based Image Retrieval’, Proceedings of the Second International Conference on Machine Learning and Cybernetics, Xi’an, (2003)

9. Kacholia Varun, Pandit Shashank, Chakrabarti Soumen, Sudarshan S., Desai Rushi, Karambelkar Hrishikesh, ‘Bidirectional Expansion For Keyword Search on Graph Databases’ ACM Proceedings of the 31st international conference on Very large data bases Trondheim, Norway (2005)

10. Najork Marc, Wiener Janet L., ‘Breadth-First Search Crawling Yields High-Quality Pages’, ACM Proceedings of the 10th international conference on World Wide Web Hong Kong, (2001)

11. Rattigan Matthew J, Maier Marc, Jensen David, ‘Graph Clustering with Network Structure Indices’, ACM Proceedings of the 24th international conference on Machine learning Corvalis, Oregon, (2007)

12. Tadikonda Satish K., Sonka Milan, Collins Steve M, ‘Efficient Coronary Border Detection Using Heuristic Graph Searching’ ieeexplore

13. Wang Yonggu, Li Xiaojuan, ‘Social Network Analysis of Interaction in Online Learning Communities’ ICALT 2007. Seventh IEEE International Conference on Advanced Learning Technologies, (2007)

14. Yushi Jing, Shumeet Baluja, ‘PageRank for Product Image Search’, WWW 2008 / Refereed Track: Rich Media, (2008)

15. Zhou Rong, Hansen Eric A, ‘Sparse-Memory Graph Search’, 18th International Joint Conference on Artificial Intelligence, Acapulco, Mexico (2003)