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...

• Type: Conference
• Year: 2003
• Where: SODA
• Authors: Surender Baswana, Ramesh Hariharan, Sandeep Sen
• Keywords: Algorithms, Hierarchical Scheme, Shortest Paths, SODA 2003, Update Time