License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.15
URN: urn:nbn:de:0030-drops-75645
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7564/
Kale, Sagar ;
Tirodkar, Sumedh
Maximum Matching in Two, Three, and a Few More Passes Over Graph Streams
Abstract
We consider the maximum matching problem in the semi-streaming model formalized by Feigenbaum, Kannan, McGregor, Suri, and Zhang that is inspired by giant graphs of today. As our main result, we give a two-pass (1/2 + 1/16)-approximation algorithm for triangle-free graphs and a two-pass (1/2 + 1/32)-approximation algorithm for general graphs; these improve the approximation ratios of 1/2 + 1/52 for bipartite graphs and 1/2 + 1/140 for general graphs by Konrad, Magniez, and Mathieu. In three passes, we achieve approximation ratios of 1/2 + 1/10 for triangle-free graphs and 1/2 + 1/19.753 for general graphs. We also give a multi-pass algorithm where we bound the number of passes precisely - we give a (2/3 - epsilon)-approximation algorithm that uses 2/(3 epsilon) passes for triangle-free graphs and 4/(3 epsilon) passes for general graphs. Our algorithms are simple and combinatorial, use O(n log(n)) space, and have O(1) update time per edge.
For general graphs, our multi-pass algorithm improves the best known deterministic algorithms in terms of the number of passes:
* Ahn and Guha give a (2/3 - epsilon)-approximation algorithm that uses O(log(1/epsilon)/epsilon^2) passes, whereas our (2/3 - epsilon)-approximation algorithm uses 4/(epsilon) passes;
* they also give a (1 - epsilon)-approximation algorithm that uses O(log(n) poly(1/epsilon)) passes, where n is the number of vertices of the input graph; although our algorithm is (2/3 - epsilon)-approximation, our number of passes do not depend on n.
Earlier multi-pass algorithms either have a large constant inside big-O notation for the number of passes or the constant cannot be determined due to the involved analysis, so our multi-pass algorithm should use much fewer passes for approximation ratios bounded slightly below 2/3.
BibTeX - Entry
@InProceedings{kale_et_al:LIPIcs:2017:7564,
author = {Sagar Kale and Sumedh Tirodkar},
title = {{Maximum Matching in Two, Three, and a Few More Passes Over Graph Streams}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
pages = {15:1--15:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-044-6},
ISSN = {1868-8969},
year = {2017},
volume = {81},
editor = {Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7564},
URN = {urn:nbn:de:0030-drops-75645},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2017.15},
annote = {Keywords: Semi Streaming, Maximum Matching}
}
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Keywords: |
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Semi Streaming, Maximum Matching |
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Collection: |
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017) |
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Issue Date: |
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2017 |
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Date of publication: |
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11.08.2017 |
