Ponencia
Searching for partial Hadamard matrices
Autor/es | Álvarez Solano, Víctor
Armario Sampalo, José Andrés Frau García, María Dolores Gudiel Rodríguez, Félix Güemes Alzaga, María Belén Martín García, Elena Osuna Lucena, Amparo |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de álgebra |
Fecha de publicación | 2010 |
Fecha de depósito | 2019-06-14 |
Publicado en |
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ISBN/ISSN | 978-84-9887-518-8 |
Resumen | Three algorithms looking for pretty large partial Hadamard ma-
trices are described. Here “large” means that hopefully about a third of a
Hadamard matrix (which is the best asymptotic result known so far, [8]) is
achieved. ... Three algorithms looking for pretty large partial Hadamard ma- trices are described. Here “large” means that hopefully about a third of a Hadamard matrix (which is the best asymptotic result known so far, [8]) is achieved. The first one performs some kind of local exhaustive search, and consequently is expensive from the time consuming point of view. The second one comes from the adaptation of the best genetic algorithm known so far searching for cliques in a graph, due to Singh and Gupta [21]. The last one consists in another heuristic search, which prioritizes the required processing time better than the final size of the partial Hadamard matrix to be obtained. In all cases, the key idea is characterizing the adjacency properties of vertices in a particular subgraph Gt of Ito’s Hadamard Graph (4t) [18], since cliques of order m in Gt can be seen as (m + 3) × 4t partial Hadamard matrices. |
Identificador del proyecto | MTM2008-06578
FQM-016 P07-FQM-02980 |
Cita | Álvarez Solano, V., Armario Sampalo, J.A., Frau García, M.D., Gudiel Rodríguez, F., Güemes Alzaga, M.B., Martín García, E. y Osuna Lucena, A. (2010). Searching for partial Hadamard matrices. En EACA 2010: XII Encuentro de Álgebra Computacional y Aplicaciones (34-39), Santiago de Compostela, España: Universidade de Santiago de Compostela, Servicio de Publicaciones. |
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