Towards a Latin-Square Search Engine

Fang, Wenxiu; Stones, Rebecca J.; Marbach, Trent G.; Wang, Gang; Liu, Xiaoguang

doi:10.1109/ispa-bdcloud-sustaincom-socialcom48970.2019.00110

Cited by 4 publications

(1 citation statement)

References 31 publications

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“…For a general reference on graph theory, see [16]. For background on latin squares, see [10,11,15]. Unless otherwise stated, k and n are positive integers.…”

Section: Introductionmentioning

confidence: 99%

Pursuit-evasion games on latin square graphs

Ahirwar¹,

Bonato²,

Leanna³

et al. 2021

Preprint

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We investigate various pursuit-evasion parameters on latin square graphs, including the cop number, metric dimension, and localization number. The cop number of latin square graphs is studied, and for k-MOLS(n), bounds for the cop number are given. If n > (k + 1) 2 , then the cop number is shown to be k + 2. Lower and upper bounds are provided for the metric dimension and localization number of latin square graphs. The metric dimension of backcirculant latin squares shows that the lower bound is close to tight. Recent results on covers and partial transversals of latin squares provide the upper bound of n + O log n log log n on the localization number of a latin square graph of order n.

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“…For a general reference on graph theory, see [16]. For background on latin squares, see [10,11,15]. Unless otherwise stated, k and n are positive integers.…”

Section: Introductionmentioning

confidence: 99%

Pursuit-evasion games on latin square graphs

Ahirwar¹,

Bonato²,

Leanna³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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Combinatorial Cryptography and Latin Squares

Zolfaghari

Bibak²

2022

Signals and Communication Technology

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Computing Autotopism Groups of Partial Latin Rectangles

Stones

Ganfornina

Kotlar

et al. 2020

ACM J. Exp. Algorithmics

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Computing the autotopism group of a partial Latin rectangle (PLR) can be performed in multiple ways. This study has two aims: comparing some of these methods experimentally to identify those that are competitive; and identifying design goals for developing practical software. We compare six families of algorithms (two backtracking and four graph-theoretic methods), with and without using entry invariants (EIs), in a range of settings. Two EIs are considered: frequencies of row, column, and symbol representatives; and 2 × 2 submatrices. The best approach to computing autotopism groups varies. When PLRs have many autotopisms (such as having very few entries or being a group table), the McKay, Meynert, and Myrvold (MMM) method computes generators for the autotopism group efficiently. (The MMM method is the standard way to compute autotopisms.) Otherwise, PLRs ordinarily have trivial or small autotopism groups, and the task is to verify this. The so-called PLR graph method is slightly more efficient in this setting than the MMM method (in some circumstances, around twice as fast). With an intermediate number of entries, the quick-to-compute strong EIs are effective at reducing the need for computation without introducing significant overhead. With a full or almost-full PLR, a more sophisticated EI is needed to reduce down-the-line computation. These results suggest a hybrid approach to computing autotopism groups: The software decides on suitable EIs based on the input; and the user chooses between the MMM or the PLR graph methods, depending on their dataset. This article expands the authors’ previous article Computing autotopism groups of PLRs: a pilot study .

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Towards a Latin-Square Search Engine

Cited by 4 publications

References 31 publications

Pursuit-evasion games on latin square graphs

Pursuit-evasion games on latin square graphs

Combinatorial Cryptography and Latin Squares

Computing Autotopism Groups of Partial Latin Rectangles

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