Ignacio Ponzoni (1,2) Mabel C. Sánchez (2) Nélida B. Brignole (2)
Keywords: graph theory, directed graphs, bipartite graphs, sparse matrices, block lower-triangular forms, assignment algorithms, partitioning algorithms.
A new partitioning algorithm that permutes sparse matrices to a specific block lower-triangular form (BlTF) complying with special features required for instrumentation problems is presented. The proposal consists in the decomposition of the occurrence matrix in two stages, using methodologies based on graph theory. First of all, Hopcroft-Karpīs algorithm is employed to match the vertices, this classification being carried out by means of a modification of Dulmage-Mendelsohnīs technique, which was devised by the authors. The second step is the application of Tarjanīs algorithm to the square blocks obtained as a result of the first stage.