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Max Cut for Random Graphs with a Planted Partition

Published online by Cambridge University Press:  24 September 2004

B. BOLLOBÁS
Affiliation:
Trinity College, Cambridge CB2 1TQ and Department of Mathematical Sciences, University of Memphis, Memphis TN38152, USA (e-mail: bollobas@msci.memphis.edu)
A. D. SCOTT
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK (e-mail: scott@math.ucl.ac.uk)

Abstract

We give an algorithm that, with high probability, recovers a planted $k$-partition in a random graph, where edges within vertex classes occur with probability $p$ and edges between vertex classes occur with probability $r\ge p+c\sqrt{p\log n/n}$. The algorithm can handle vertex classes of different sizes and, for fixed $k$, runs in linear time. We also give variants of the algorithm for partitioning matrices and hypergraphs.

Type
Research Article
Copyright
© 2004 Cambridge University Press

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