Fully dynamic maximal matching in O(log n) update time
Abstract
We present an algorithm for maintaining maximal matching in a graph under addition and deletion of edges. Our data structure is randomized that takes O(log n) expected amortized time for each edge update where n is the number of vertices in the graph. While there is a trivial O(n) algorithm for edge update, the previous best known result for this problem for a graph with n vertices and m edges is O({(n+ m)}^{0.7072})which is sub-linear only for a sparse graph. For the related problem of maximum matching, Onak and Rubinfield designed a randomized data structure that achieves O(log^2 n) amortized time for each update for maintaining a c-approximate maximum matching for some large constant c. In contrast, we can maintain a factor two approximate maximum matching in O(log n) expected time per update as a direct corollary of the maximal matching scheme. This in turn also implies a two approximate vertex cover maintenance scheme that takes O(log n) expected time per update.
Cite
@article{arxiv.1103.1109,
title = {Fully dynamic maximal matching in O(log n) update time},
author = {Surender Baswana and Manoj Gupta and Sandeep Sen},
journal= {arXiv preprint arXiv:1103.1109},
year = {2016}
}
Comments
16 pages, 3 figures