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A Simple SVD Algorithm for Finding Hidden Partitions

Part of: Algorithms - Computer Science Combinatorial probability Theory of computing

Published online by Cambridge University Press:  09 October 2017

VAN VU
VAN VU*
Affiliation:
Department of Mathematics, Yale, New Haven, CT 06520, USA (e-mail van.vu@yale.edu)
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Abstract

Finding a hidden partition in a random environment is a general and important problem which contains as subproblems many important questions, such as finding a hidden clique, finding a hidden colouring, finding a hidden bipartition, etc.

In this paper we provide a simple SVD algorithm for this purpose, addressing a question of McSherry. This algorithm is easy to implement and works for sparse graphs under optimal density assumptions. We also consider an approximating algorithm, which on one hand works under very mild assumptions, but on other hand can sometimes be upgraded to give the exact solution.

MSC classification

Primary: 68Q87: Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)
Secondary: 68W20: Randomized algorithms 60C05: Combinatorial probability

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Issue 1 , January 2018 , pp. 124 - 140
Copyright
Copyright © Cambridge University Press 2017 

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