🤖 AI Summary
This work addresses the high computational complexity and limited scalability in enumerating non-OD-equivalence classes of large orthogonal arrays—specifically OA(128,9,2,4), OA(144,9,2,4), and OA(192,k,2,4) for k=9,10,11—by proposing a parallelized branch-and-bound algorithm. The method integrates Margot’s isomorphism pruning strategy with symmetry reduction techniques to drastically shrink the search space. It achieves, for the first time, a complete classification of OA(192,k,2,4) for k=9,10,11, and demonstrates near-linear speedup on OA(128,9,2,4) and OA(144,9,2,4). These results overcome the scalability limitations of serial approaches and confirm the algorithm’s efficiency and practicality in tackling large-scale orthogonal array enumeration problems.
📝 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.