Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs

Mateva, Zlatka. "Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs." Serdica Journal of Computing 2.4 (2008): 349-368. <http://eudml.org/doc/11472>.

@article{Mateva2008,
abstract = {Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.The author developed computer programs needed for the classification of designs with certain automorphisms by the local approach method. All these programs use canonicity test or/and construction of canonical form of an integer matrix. Their efficiency substantially influences the speed of the whole computation. The present paper deals with the implemented canonicity algorithm. It is based on ideas used by McKay, Meringer, Kaski and Bouyukliev, but while their algorithms are for the equivalence test, the canonicity test or finding canonical representative of only one type of combinatorial object (graph, code, design, binary matrix, etc.), the algorithm presented in this paper is meant to work fast on all types of integer matrices used for the classification of designs with predefined automorphisms. This is achieved through the suitable spectrum invariant, and the way it is used to cut off some branches of the search tree.},
author = {Mateva, Zlatka},
journal = {Serdica Journal of Computing},
keywords = {Algorithm; Automorphism; Incidence Matrix; Orbit Matrix; Group Action; Canonical Form; BIBD; algorithm; automorphism; incidence matrix; orbit matrix; group action; canonical form},
language = {eng},
number = {4},
pages = {349-368},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs},
url = {http://eudml.org/doc/11472},
volume = {2},
year = {2008},
}

TY - JOUR
AU - Mateva, Zlatka
TI - Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs
JO - Serdica Journal of Computing
PY - 2008
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 2
IS - 4
SP - 349
EP - 368
AB - Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.The author developed computer programs needed for the classification of designs with certain automorphisms by the local approach method. All these programs use canonicity test or/and construction of canonical form of an integer matrix. Their efficiency substantially influences the speed of the whole computation. The present paper deals with the implemented canonicity algorithm. It is based on ideas used by McKay, Meringer, Kaski and Bouyukliev, but while their algorithms are for the equivalence test, the canonicity test or finding canonical representative of only one type of combinatorial object (graph, code, design, binary matrix, etc.), the algorithm presented in this paper is meant to work fast on all types of integer matrices used for the classification of designs with predefined automorphisms. This is achieved through the suitable spectrum invariant, and the way it is used to cut off some branches of the search tree.
LA - eng
KW - Algorithm; Automorphism; Incidence Matrix; Orbit Matrix; Group Action; Canonical Form; BIBD; algorithm; automorphism; incidence matrix; orbit matrix; group action; canonical form
UR - http://eudml.org/doc/11472
ER -