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 | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-10-10291-3

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.