Computing autotopism groups of partial Latin rectangles: A pilot study
Computing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one should have in mind for developing practical software. To this end, we compare six f...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/105208 |
| Acceso en línea: | https://hdl.handle.net/11441/105208 https://doi.org/10.1002/cmm4.1094 |
| Access Level: | acceso abierto |
| Palabra clave: | Autotopism Latin square Partial Latin rectangle |
| Sumario: | Computing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one should have in mind for developing practical software. To this end, we compare six families of algorithms (two backtracking methods and four graph automorphism methods), with and without the use of entry invariants, on two test suites. We consider two entry invariants: one determined by the frequencies of row, column, and symbol representatives, and one determined by 2 2 submatrices. We nd: (a) with very few entries, many symmetries often exist, and these should be identi ed mathematically rather than computationally, (b) with an intermediate number of entries, a quick-to-compute entry invariant was e ective at reducing the need for computation, (c) with an almost-full partial Latin rectangle, more sophisticated entry invariants are needed, and (d) the performance for (full) Latin squares is signi cantly poorer than other partial Latin rectangles of comparable size, obstructed by the existence of Latin squares with large (possibly transitive) autotopism groups. |
|---|