Parallelizing the branch-and-bound with isomorphism pruning algorithm for classifying orthogonal arrays

TL;DR

This paper introduces a parallelization method for an isomorphism pruning algorithm used in classifying orthogonal arrays, achieving significant speedups and enabling new classifications.

Contribution

A novel parallelization approach for the branch-and-bound with isomorphism pruning algorithm applied to orthogonal array classification.

Findings

Achieved linear speedups in classifying certain orthogonal arrays.

Enabled the classification of all non-OD-equivalent OA(192, k, 2, 4) for k=9,10,11 for the first time.

Abstract

We provide a method for parallelizing the branch-and-bound with isomorphism pruning algorithm developed by Margot [Symmetric ILP: Coloring and small integers, Discrete Optimization (4) (2007), 40-62]. We apply our method to classify orthogonal arrays. For classifying all non-OD- equivalent OA(128, 9, 2, 4) and OA(144, 9, 2, 4) our method results in linear speedups. Finally, our method enables classifying all non-OD-equivalent OA(192, k, 2, 4) for k = 9, 10, 11 for the first time.