Strong external difference families in abelian and non-abelian groups

Huczynska, Sophie; Jefferson, Christopher; Silvia, Nepsinska,

doi:10.1007/s12095-021-00473-3

Cited by 7 publications

(2 citation statements)

References 12 publications

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“…For the purposes of this paper, a group is a set G with an associative and invertible binary operation ×. Also, G must contain an identity element e, which means that e × g = g for every g ∈ G. The model of SEDF described below (with additional symmetry breaking constraints) was used to find a number of previously undiscovered SEDFs, including the first in non-Abelian groups [44].…”

Section: Strong External Difference Familiesmentioning

confidence: 99%

Automatic Tabulation in Constraint Models

Akgün¹,

Gent²,

Jefferson³

et al. 2022

Preprint

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The performance of a constraint model can often be improved by converting a subproblem into a single table constraint. In this paper we study heuristics for identifying promising candidate subproblems, where converting the candidate into a table constraint is likely to improve solver performance. We propose a small set of heuristics to identify common cases, such as expressions that will propagate weakly. The process of discovering promising subproblems and tabulating them is entirely automated in the constraint modelling tool Savile Row. Caches are implemented to avoid tabulating equivalent subproblems many times. We give a simple algorithm to generate table constraints directly from a constraint expression in Savile Row. We demonstrate good performance on the benchmark problems used in earlier work on tabulation, and also for several new problem classes. In some cases, the entirely automated process leads to orders of magnitude improvements in solver performance.Note to reviewers and editor: This paper builds on (and entirely includes) an earlier conference publication [1]. We have extended and refined the method and also performed a much more extensive experimental evaluation.

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Section: Strong External Difference Familiesmentioning

confidence: 99%

Automatic Tabulation in Constraint Models

Akgün¹,

Gent²,

Jefferson³

et al. 2022

Preprint

Self Cite

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“…In nonabelian groups, while the definitions of these difference family‐type structures remain valid, very little is known. There are just a few nonabelian EDFs in the literature (see, e.g., [19]), and before this paper there were no known constructions for nonabelian DPDFs or EPDFs, so the nonabelian constructions presented here are significant.…”

Section: Introductionmentioning

confidence: 99%

New constructions for disjoint partial difference families and external partial difference families

Huczynska,

Johnson

2024

J of Combinatorial Designs

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Recently, new combinatorial structures called disjoint partial difference families (DPDFs) and external partial difference families (EPDFs) were introduced, which simultaneously generalize partial difference sets, disjoint difference families and external difference families, and have applications in information security. So far, all known construction methods have used cyclotomy in finite fields. We present the first noncyclotomic infinite families of DPDFs which are also EPDFs, in structures other than finite fields (in particular cyclic groups and nonabelian groups). As well as direct constructions, we present an approach to constructing DPDFs/EPDFs using relative difference sets (RDSs); as part of this, we demonstrate how the well‐known RDS result of Bose extends to a very natural construction for DPDFs and EPDFs.

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Decomposing Complete Graphs into Isomorphic Complete Multipartite Graphs

Huczynska,

Paterson

2012

Fields Institute Communications

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Strong external difference families in abelian and non-abelian groups

Cited by 7 publications

References 12 publications

Automatic Tabulation in Constraint Models

Automatic Tabulation in Constraint Models

New constructions for disjoint partial difference families and external partial difference families

Decomposing Complete Graphs into Isomorphic Complete Multipartite Graphs

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