Please use this identifier to cite or link to this item:
http://dx.doi.org/10.25673/79803
Title: | Permutation group algorithms based on directed graphs |
Author(s): | Jefferson, Christopher Pfeiffer, Markus Wilson, Wilf A. Waldecker, Rebecca ![]() |
Issue Date: | 2021 |
Type: | Article |
Language: | English |
Abstract: | 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 GraphBacktracking package for GAP. |
URI: | https://opendata.uni-halle.de//handle/1981185920/81757 http://dx.doi.org/10.25673/79803 |
Open Access: | ![]() |
License: | ![]() |
Sponsor/Funder: | Publikationsfonds MLU |
Journal Title: | Journal of algebra |
Publisher: | Elsevier |
Publisher Place: | San Diego, Calif. |
Volume: | 585 |
Original Publication: | 10.1016/j.jalgebra.2021.06.015 |
Page Start: | 723 |
Page End: | 758 |
Appears in Collections: | Open Access Publikationen der MLU |
Files in This Item:
File | Description | Size | Format | |
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1-s2.0-S0021869321003240-main.pdf | 743.12 kB | Adobe PDF | ![]() View/Open |