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2002
ACM

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

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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...
Surender Baswana, Ramesh Hariharan, Sandeep Sen
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2002
Where STOC
Authors Surender Baswana, Ramesh Hariharan, Sandeep Sen
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