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SODA
2003
ACM

Maintaining all-pairs approximate shortest paths under deletion of edges

9 years 13 days ago
Maintaining all-pairs approximate shortest paths under deletion of edges
We present a hierarchical scheme for efficiently maintaining all-pairs approximate shortest-paths in undirected unweighted graphs under deletions of edges. An α-approximate shortest-path between two vertices is a path of length at-most α times the length of the shortest path. For maintaining α-approximate shortest paths for all pairs of vertices separated by distance ≤ d in a graph of n vertices, we present the first o(nd) update time algorithm based on our hierarchical scheme. In particular, the update time per edge deletion achieved by our algorithm is ˜O(min{ √ nd, (nd)2/3 }) for 3approximate shortest-paths, and ˜O(min{ 3 √ nd, (nd)4/7 }) for 7-approximate shortest-paths. For graphs with θ(n2 ) edges, we achieve even further improvement in update time : ˜O( √ nd) for 3-approximate shortest-paths, and ˜O( 3 √ nd2) for 5-approximate shortest-paths. For maintaining all-pairs approximate shortestpaths, we improve the previous ˜O(n3/2 ) bound on the update time per e...
Surender Baswana, Ramesh Hariharan, Sandeep Sen
Added 01 Nov 2010
Updated 01 Nov 2010
Type Conference
Year 2003
Where SODA
Authors Surender Baswana, Ramesh Hariharan, Sandeep Sen
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