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### Improved Approximation Guarantees for Weighted Matching in the Semi-Streaming Model

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### Abstract

We study the maximum weight matching problem in the semi-streaming model, and improve on the currently best one-pass algorithm due to Zelke (Proc.\ STACS~'08, pages 669--680) by devising a deterministic approach whose performance guarantee is $4.91 + \eps$. In addition, we study {\em preemptive} online algorithms, a sub-class of one-pass algorithms where we are only allowed to maintain a feasible matching in memory at any point in time. All known results prior to Zelke's belong to this sub-class. We provide a lower bound of $4.967$ on the competitive ratio of any such deterministic algorithm, and hence show that future improvements will have to store in memory a set of edges which is not necessarily a feasible matching. We conclude by presenting an empirical study, conducted in order to compare the practical performance of our approach to that of previously suggested algorithms.

### BibTeX - Entry

@InProceedings{epstein_et_al:LIPIcs:2010:2476,
author =	{Leah Epstein and Asaf Levin and Juli{\'a}n Mestre and Danny Segev},
title =	{{Improved Approximation Guarantees for Weighted Matching in the Semi-Streaming Model}},
booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
pages =	{347--358},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-16-3},
ISSN =	{1868-8969},
year =	{2010},
volume =	{5},
editor =	{Jean-Yves Marion and Thomas Schwentick},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},