Randomized Greedy Algorithms for the Maximum Matching Problem with New Analysis

Author

Poloczek, Matthias ; Szegedy, Mario

Author_Institution

Inst. of Comput. Sci., Goethe Univ., Frankfurt, Germany

fYear

2012

fDate

20-23 Oct. 2012

Firstpage

708

Lastpage

717

Abstract

It is a long-standing problem to lower bound the performance of randomized greedy algorithms for maximum matching. Aronson, Dyer, Frieze and Suen [1]studied the modified randomized greedy (MRG) algorithm and proved that it approximates the maximum matching within a factor of at least 1/2 + 1/400,000. They use heavy combinatorial methods in their analysis. We introduce a new technique we call Contrast Analysis, and show a 1/2 + 1/256 performance lower bound for the MRG algorithm. The technique seems to be useful not only for the MRG, but also for other related algorithms.

Keywords

approximation theory; combinatorial mathematics; greedy algorithms; randomised algorithms; MRG algorithm; approximation; combinatorial methods; contrast analysis; long-standing problem; maximum matching problem; modified randomized greedy algorithm; Algorithm design and analysis; Approximation algorithms; Approximation methods; Greedy algorithms; Schedules; Tin; Weapons; approximation; greedy; matching; randomized;

fLanguage

English

Publisher

ieee

Conference_Titel

Foundations of Computer Science (FOCS), 2012 IEEE 53rd Annual Symposium on

Conference_Location

New Brunswick, NJ

ISSN

0272-5428

Print_ISBN

978-1-4673-4383-1

Type

conf

DOI

10.1109/FOCS.2012.20

Filename

6375350