Bhattacharya, Sayan ;
Gupta, Manoj ;
Mohan, Divyarthi
Improved Algorithm for Dynamic b-Matching
Abstract
Recently there has been extensive work on maintaining (approximate) maximum matchings in dynamic graphs. We consider a generalisation of this problem known as the maximum b-matching: Every node v has a positive integral capacity b_v, and the goal is to maintain an (approximate) maximum-cardinality subset of edges that contains at most b_v edges incident on every node v. The maximum matching problem is a special case of this problem where b_v = 1 for every node v.
Bhattacharya, Henzinger and Italiano [ICALP 2015] showed how to maintain a O(1) approximate maximum b-matching in a graph in O(log^3 n) amortised update time. Their approximation ratio was a large (double digit) constant. We significantly improve their result both in terms of approximation ratio as well as update time. Specifically, we design a randomised dynamic algorithm that maintains a (2+epsilon)-approximate maximum $b$-matching in expected amortised O(1/epsilon^4) update time. Thus, for every constant epsilon in (0, 1), we get expected amortised O(1) update time. Our algorithm generalises the framework of Baswana, Gupta, Sen [FOCS 2011] and Solomon [FOCS 2016] for maintaining a maximal matching in a dynamic graph.
BibTeX - Entry
@InProceedings{bhattacharya_et_al:LIPIcs:2017:7844,
author = {Sayan Bhattacharya and Manoj Gupta and Divyarthi Mohan},
title = {{Improved Algorithm for Dynamic b-Matching}},
booktitle = {25th Annual European Symposium on Algorithms (ESA 2017)},
pages = {15:1--15:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-049-1},
ISSN = {1868-8969},
year = {2017},
volume = {87},
editor = {Kirk Pruhs and Christian Sohler},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7844},
URN = {urn:nbn:de:0030-drops-78443},
doi = {10.4230/LIPIcs.ESA.2017.15},
annote = {Keywords: dynamic data structures, graph algorithms}
}
Keywords: |
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dynamic data structures, graph algorithms |
Seminar: |
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25th Annual European Symposium on Algorithms (ESA 2017)
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Issue date: |
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2017 |
Date of publication: |
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01.09.2017 |
01.09.2017