Parallelizing the branch-and-bound with isomorphism pruning algorithm for classifying orthogonal arrays
Provides a parallelization method for a known algorithm, enabling new classifications in combinatorial design theory.
The paper parallelizes a branch-and-bound with isomorphism pruning algorithm to classify orthogonal arrays, achieving linear speedups for OA(128,9,2,4) and OA(144,9,2,4), and enabling first-time classification of OA(192,k,2,4) for k=9,10,11.
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.