Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths

We present improved algorithms for maintaining transitive closure and all-pairs shortest paths/distances in a digraph under deletion of edges. For the problem of transitive closure, the previous best known algorithms, for achieving O(1) query time, require O(min(m, n3 m )) amortized update time, implying an upper bound of O(n 3 2 ) on update time per edge-deletion. We present an algorithm that achieves O(1) query time and O(n log2 n+ n2 m log n) update time per edge-deletion, thus improving the upper bound to O(n 4 3 3 log n). For the problem of maintaining all-pairs shortest distances in unweighted digraph under deletion of edges, we present an algorithm that requires O(n3 m log2 n) amortized update time and answers a distance query in O(1) time. This improves the previous best known update bound by a factor of log n. For maintaining all-pairs shortest paths, we present an algorithm that achieves O(min(n 3 2 log n, n3 m log2 n)) amortized update time and reports a shortest path i...

• Type: Conference
• Year: 2002
• Where: STOC
• Authors: Surender Baswana, Ramesh Hariharan, Sandeep Sen
• Keywords: Algorithms, All-pairs Shortest, Log N, STOC 2002, Update Time