Graph Colouring and Branch and Bound Approaches for Permutation Code Algorithms

Abstract

A considerable amount of research has been devoted to permutation codes in recent years. This has been motivated by some real-world applications. Permutation codes are important because of their robustness against transmission errors and noise. This study addresses the problem of the construction of the largest possible permutation codes with given parameters, namely a specified length and minimum Hamming distance. The problem is modelled in terms of maximum cliques and it is shown how a well-known upper bound based on colouring can be successfully embedded inside a branch and bound method. Experimental results are presented to evaluate the effectiveness of the new idea.