A Parallel Branch and Bound Algorithm for the Maximum Labelled Clique Problem

TL;DR

This paper presents a new parallel branch-and-bound algorithm for the maximum labelled clique problem, significantly improving solution speed and efficiency over previous methods through effective parallelization and optimization.

Contribution

The paper introduces a novel parallel branch-and-bound algorithm specifically designed for the maximum labelled clique problem, demonstrating substantial performance improvements.

Findings

Algorithm is consistently faster than previous methods

Achieves speedups of four to five orders of magnitude on benchmarks

Effective parallelization enhances solution efficiency

Abstract

The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new branch-and-bound algorithm for the problem, and explain how it may be parallelised. We evaluate an implementation on a set of benchmark instances, and show that it is consistently faster than previously published results, sometimes by four or five orders of magnitude.