Perfect refiners for permutation group backtracking algorithms
Abstract
Backtrack search is a fundamental technique for computing with finite permutation groups, which has been formulated in terms of points, ordered partitions, and graphs. We provide a framework for discussing the most common forms of backtrack search in a generic way. We introduce the concept of perfect refiners to better understand and compare the pruning power available in these different settings. We also present a new formulation of backtrack search, which allows the use of graphs with additional vertices, and which is implemented in the software package VOLE. For each setting, we classify the groups and cosets for which there exist perfect refiners. Moreover, we describe perfect refiners for many naturally-occurring examples of stabilisers and transporter sets, including applications to normaliser and subgroup conjugacy problems for 2-closed groups.
Citation
Jefferson , C , Waldecker , R & Wilson , W A 2023 , ' Perfect refiners for permutation group backtracking algorithms ' , Journal of Symbolic Computation , vol. 114 , pp. 18-36 . https://doi.org/10.1016/j.jsc.2022.04.007
Publication
Journal of Symbolic Computation
Status
Peer reviewed
ISSN
0747-7171Type
Journal article
Description
We therefore thank the VolkswagenStiftung (Grant no. 93764 ) and the Royal Society (Grant code URF\R\180015) again for their financial support of this earlier work. For financial support during the more recent advances, we thank the DFG (Grant no. WA 3089/9-1) and again the Royal Society (Grant codes RGF\EA\181005 and URF\R\180015 ).Collections
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