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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Borel oracles. An analytical approach to constant-time algorithms


Authors: Gábor Elek and Gábor Lippner
Journal: Proc. Amer. Math. Soc. 138 (2010), 2939-2947
MSC (2000): Primary 03E15; Secondary 68R10
Published electronically: April 15, 2010
MathSciNet review: 2644905
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Abstract: In 2008 Nguyen and Onak constructed the first constant-time algorithm for the approximation of the size of the maximum matching in bounded degree graphs. The Borel oracle machinery is a tool that can be used to convert some statements in Borel graph theory to theorems in the field of constant-time algorithms. In this paper we illustrate the power of this tool to prove the existence of the above mentioned constant-time approximation algorithm.


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Additional Information

Gábor Elek
Affiliation: Alfred Renyi Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364, Budapest, Hungary
Email: elek@renyi.hu

Gábor Lippner
Affiliation: Department of Computer Science, Eötvös University, Pázmány Péter sétány 1/C, H-117, Budapest, Hungary
Email: lipi@cs.elte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10291-3
PII: S 0002-9939(10)10291-3
Keywords: Constant time algorithms, graph limits, Borel graphs, invariant measures, maximum matching
Received by editor(s): July 18, 2009
Received by editor(s) in revised form: November 14, 2009
Published electronically: April 15, 2010
Additional Notes: The first author’s research was sponsored by OTKA Grant 67867
The second author’s research was sponsored by OTKA Grant 69062
Communicated by: Julia Knight
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.