Exact and approximative algorithms for coloring G(n,p)

  1. Amin Coja-Oghlan,
  2. Anusch Taraz*

Article first published online: 1 MAR 2004

DOI: 10.1002/rsa.20007

Issue

Random Structures & Algorithms

Random Structures & Algorithms

Special Issue: Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I

Volume 24, Issue 3, pages 259–278, May 2004

Additional Information

How to Cite

Coja-Oghlan, A. and Taraz, A. (2004), Exact and approximative algorithms for coloring G(n,p). Random Structures & Algorithms, 24: 259–278. doi: 10.1002/rsa.20007

Author Information

  1. Humboldt-Universität zu Berlin, Institut für Informatik, Unter den Linden 6, 10099 Berlin, Germany

*Humboldt-Universität zu Berlin, Institut für Informatik, Unter den Linden 6, 10099 Berlin, Germany

Publication History

  1. Issue published online: 26 MAR 2004
  2. Article first published online: 1 MAR 2004
  3. Manuscript Accepted: 9 OCT 2003
  4. Manuscript Received: 31 DEC 2002

Funded by

  • Deutsche Forschungsgemeinschaft. Grant Number: DFG FOR 413/1-1

SEARCH

SEARCH BY CITATION

ARTICLE TOOLS

Get PDF (183K)

Abstract

We investigate the problem of coloring random graphs G(n, p) in polynomial expected time. For the case p ≤ 1.01/n, we present an algorithm that finds an optimal coloring in linear expected time. For p ≫ ln6(n)/n, we give algorithms which approximate the chromatic number within a factor of O( equation image). We also obtain an O(equation image/ln(np))-approximation algorithm for the independence number. As an application, we propose an algorithm for deciding satisfiability of random 2k-SAT formulas over n propositional variables with ≥ ln7(n)nk clauses in polynomial expected time. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004

Get PDF (183K)