Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs (1999)
| Venue: | IN PROC. 40TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS’99 |
| Citations: | 49 - 0 self |
BibTeX
@INPROCEEDINGS{King99fullydynamic,
author = {Valerie King},
title = {Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs},
booktitle = {IN PROC. 40TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS’99},
year = {1999},
pages = {81--91},
publisher = {}
}
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Abstract
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 + ffl), for any positive constant ffl, the amortized update time is O(n 2 log 2 n= log log n); for an error factor of (1 + ffl) the amortized update time is O(n 2 log 3 (bn)=ffl 2 ). For exact shortest paths the amortized update time is O(n 2:5 p b log n). Query time for exact and approximate shortest distances is O(1); exact 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(n 2 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(n 2:28 ). The algorithms use simple data structures, and are deterministic.
