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Top-k shortest path

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The document proposes a new method for efficiently finding the top-k shortest simple paths between two nodes in a graph. It precomputes shortest path trees, transforms the graph, and uses optimizations like k-reduction and adaptive thresholds to terminate path searches early. Experimental results on real and synthetic graphs show the method outperforms prior algorithms by Yen and Hershberger for discovering top-k shortest paths.

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Fast Top-k Simple Shortest Paths Discovery in Graphs Database Research Group Department of Computer Science Peking University Jun Gao, Huida Qiu, Xiao Jiang, Dongqing Yang, Tenjiao Wang
[object Object],[object Object],[object Object],[object Object],[object Object],Outline
Motivation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Top k shortest paths query ,[object Object],[object Object],[object Object],[object Object],1 1 1 1 1 3 3 1 2 3 4 5 6 ,[object Object],[object Object],[object Object],[object Object],1
[object Object],[object Object],[object Object],[object Object],[object Object],Outline
Top K genenal shortest path problem ,[object Object],[object Object],[object Object],[object Object],[object Object],Original Graph Shortest Path Tree Side Cost on Edges
Top K loopless Shortest Path Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Candidate Paths
Top K loopless Shortest Path Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Candidate Paths
[object Object],[object Object],[object Object],[object Object],[object Object],Outline
Basic Idea ,[object Object],[object Object],[object Object],[object Object],[object Object]
Graph Pre-processing Precompute the shortest path tree rooted at t Make side cost of each edge Assign (pre, post, parent) encoding on each node to accelarate the loop detection
Searching for the candidate paths ,[object Object],[object Object],[object Object],[object Object],Starting Node
Path Searching Example ,[object Object],[object Object],[object Object],[object Object]
Optimization-1 ,[object Object],[object Object],[object Object],[object Object]
Optimization-2 ,[object Object],[object Object],[object Object]
Optimization-2 ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],Outline
Experimental Evaluation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Datasets ,[object Object],[object Object],[object Object],Dataset # of Nodes # of Edges Density Add32 4,960 9,462 1.91 Crack 10,240 30,380 2.97 Gupta3 16,783 4,670,105 278.26 FLA 1,070,376 2,712,798 2.53
Impact of Graph Size ,[object Object]
Impact of k ,[object Object]
Impact of Density ,[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],Outline
Conclusion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Future work ,[object Object],[object Object],[object Object]
Thanks for your attention! ,[object Object]

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Top-k shortest path

  • 1. Fast Top-k Simple Shortest Paths Discovery in Graphs Database Research Group Department of Computer Science Peking University Jun Gao, Huida Qiu, Xiao Jiang, Dongqing Yang, Tenjiao Wang
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  • 11. Graph Pre-processing Precompute the shortest path tree rooted at t Make side cost of each edge Assign (pre, post, parent) encoding on each node to accelarate the loop detection
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