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Algorithms 2012, 5(4), 545-587; doi:10.3390/a5040545

Exact Algorithms for Maximum Clique: A Computational Study 

Computing Science, University of Glasgow, Glasgow G12 8QQ, UK
Received: 11 September 2012 / Revised: 29 October 2012 / Accepted: 29 October 2012 / Published: 19 November 2012
(This article belongs to the Special Issue Graph Algorithms)
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We investigate a number of recently reported exact algorithms for the maximum clique problem. The program code is presented and analyzed to show how small changes in implementation can have a drastic effect on performance. The computational study demonstrates how problem features and hardware platforms influence algorithm behaviour. The effect of vertex ordering is investigated. One of the algorithms (MCS) is broken into its constituent parts and we discover that one of these parts frequently degrades performance. It is shown that the standard procedure used for rescaling published results (i.e., adjusting run times based on the calibration of a standard program over a set of benchmarks) is unsafe and can lead to incorrect conclusions being drawn from empirical data.
Keywords: maximum clique; exact algorithms; empirical study  maximum clique; exact algorithms; empirical study 
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Prosser, P. Exact Algorithms for Maximum Clique: A Computational Study . Algorithms 2012, 5, 545-587.

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