Permutation group algorithms based on directed graphs
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We introduce a new framework for solving an important class of computational problems involving finite permutation groups, which includes calculating set stabilisers, intersections of subgroups, and isomorphisms of combinatorial structures. Our techniques are inspired by and generalise 'partition backtrack', which is the current state-of-the-art algorithm introduced by Jeffrey Leon in 1991. But, instead of ordered partitions, we use labelled directed graphs to organise our backtrack search algorithms, which allows for a richer representation of many problems while often resulting in smaller search spaces. In this article we present the theory underpinning our framework, we describe our algorithms, and we show the results of some experiments. An implementation of our algorithms is available as free software in the Graph Back tracking package for GAP.
Jefferson , C , Pfeiffer , M , Wilson , W A & Waldecker , R 2021 , ' Permutation group algorithms based on directed graphs ' , Journal of Algebra , vol. 585 , pp. 723-758 . https://doi.org/10.1016/j.jalgebra.2021.06.015
Journal of Algebra
Copyright © 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license
DescriptionFunding: The authors would like to thank the DFG (Grant no. WA 3089/6-1) and the VolkswagenStiftung (Grant no. 93764) for financially supporting this work and projects leading up to it. The first and third authors are supported by the Royal Society (Grant codes RGF\EA\181005 and URF\R\180015).
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