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Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs

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1 Author(s)
King, V. ; Dept. of Comput. Sci., Victoria Univ., BC, Canada

This paper presents the first fully dynamic algorithms for maintaining all-pairs shortest paths in digraphs with positive integer weights less than b. For approximate shortest paths with an error factor of (2+ε), for any positive constant ε, the amortized update time is O(n2 log2 n/log log n); for an error factor of (1+ε) the amortized update time is O(n2 log 3 (bn)/ε2). For exact shortest paths the amortized update time is O(n2.5 √(b log n)). Query time for exact and approximate shortest distances is O(1); exact time and approximate paths can be generated in time proportional to their lengths. Also presented is a fully dynamic transitive closure algorithm with update time O(n2 log n) and query time O(1). The previously known fully dynamic transitive closure algorithm with fast query time has one-sided error and update time O(n2.28). The algorithms use simple data structures, and are deterministic

Published in:

Foundations of Computer Science, 1999. 40th Annual Symposium on

Date of Conference:

1999