Exact Algorithms for Maximum Clique: a computational study

TL;DR

This paper evaluates various exact algorithms for the maximum clique problem, highlighting how implementation details, problem features, and hardware influence performance, and critiques current benchmarking practices.

Contribution

It provides a detailed computational comparison of recent algorithms, analyzes the impact of implementation choices, and questions standard result rescaling methods.

Findings

Small implementation changes drastically affect performance

Problem features and hardware influence algorithm behavior

Rescaling published results can be unsafe

Abstract

We investigate a number of recently reported exact algorithms for the maximum clique problem (MCQ, MCR, MCS, BBMC). The program code used is presented and critiqued showing 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 minimum width order (smallest-last) is investigated, and MCS is broken into its consituent parts and we discover that one of these parts degrades performance. It is shown that the standard procedure used for rescaling published results is unsafe.