When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2018.39
URN: urn:nbn:de:0030-drops-99383
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9938/
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### Deterministic Algorithms for Maximum Matching on General Graphs in the Semi-Streaming Model

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### Abstract

We present an improved deterministic algorithm for Maximum Cardinality Matching on general graphs in the Semi-Streaming Model. In the Semi-Streaming Model, a graph is presented as a sequence of edges, and an algorithm must access the edges in the given sequence. It can only use O(n polylog n) space to perform computations, where n is the number of vertices of the graph. If the algorithm goes over the stream k times, it is called a k-pass algorithm. In this model, McGregor [McGregor, 2005] gave the currently best known randomized (1+epsilon)-approximation algorithm for maximum cardinality matching on general graphs, that uses (1/epsilon)^{O(1/epsilon)} passes. Ahn and Guha [Ahn and Guha, 2013] later gave the currently best known deterministic (1+epsilon)-approximation algorithms for maximum cardinality matching: one on bipartite graphs that uses O(log log(1/epsilon)/epsilon^2) passes, and the other on general graphs that uses O(log n *poly(1/epsilon)) passes (note that, for general graphs, the number of passes is dependent on the size of the input). We present the first deterministic algorithm that achieves a (1+epsilon)-approximation on general graphs in only a constant number ((1/epsilon)^{O(1/epsilon)}) of passes.

### BibTeX - Entry

```@InProceedings{tirodkar:LIPIcs:2018:9938,
author =	{Sumedh Tirodkar},
title =	{{Deterministic Algorithms for Maximum Matching on General Graphs in the Semi-Streaming Model}},
booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
pages =	{39:1--39:16},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-093-4},
ISSN =	{1868-8969},
year =	{2018},
volume =	{122},
editor =	{Sumit Ganguly and Paritosh Pandya},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},