Sampling to provide or to bound: With applications to fully dynamic graph algorithms

Abstract

In dynamic graph algorithms the following provide-or-bound problem has to be solved quickly: Given a set S containing a subset R and a way of generating random elements from S testing for membership in R, either (i) provide an element of R or (ii) give a (small) upper bound on the size of R that holds with high probability. We give an optimal algorithm for this problem. This algorithm improves the time per operation for various dyamic graph algorithms by a factor of O(log n). For example, it improves the time per update for fully dynamic connectivity from O(log 3 n) to O(log 2 n).

DOI: 10.1002/(SICI)1098-2418(199712)11:4%3C369::AID-RSA5%3E3.0.CO;2-X

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Cite this paper

@article{Henzinger1997SamplingTP, title={Sampling to provide or to bound: With applications to fully dynamic graph algorithms}, author={Monika Henzinger and Mikkel Thorup}, journal={Random Struct. Algorithms}, year={1997}, volume={11}, pages={369-379} }