DocumentCode :
2723235
Title :
Fully Dynamic Maximal Matching in O (log n) Update Time
Author :
Baswana, Surender ; Gupta, Manoj ; Sen, Sandeep
Author_Institution :
Dept. of CSE, I.I.T. Kanpur, Kanpur, India
fYear :
2011
fDate :
22-25 Oct. 2011
Firstpage :
383
Lastpage :
392
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 was due to Ivkovic and Llyod[4]. For a graph with n vertices and m edges, they give an O((n + m)0.7072) update time algorithm which is sublinear only for a sparse graph. For the related problem of maximum matching, Onak and Rubinfeld [6] designed a randomized data structure that achieves O(log2 n) expected 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 amortized 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 amortized time per update.
Keywords :
approximation theory; graph theory; O(log n) update time; approximate vertex cover maintenance scheme; c-approximate maximum matching; edge deletion; edge update; expected amortized time; fully dynamic maximal matching; sparse graph; Algorithm design and analysis; Approximation algorithms; Approximation methods; Computational efficiency; Data structures; Heuristic algorithms; Partitioning algorithms;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Foundations of Computer Science (FOCS), 2011 IEEE 52nd Annual Symposium on
Conference_Location :
Palm Springs, CA
ISSN :
0272-5428
Print_ISBN :
978-1-4577-1843-4
Type :
conf
DOI :
10.1109/FOCS.2011.89
Filename :
6108199
Link To Document :
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