Permutation of Sparse Matrices to a Specific Lower BTF using Graph Decompositions

Ignacio Ponzoni (1,2) Mabel C. Sánchez (2) Nélida B. Brignole (2)

  1. Departamento de Ciencias de la Computación - Universidad Nacional del Sur Avda. Alem 1253 - 8000 Bahía Blanca - Argentina Planta Piloto de Ingeniería Química - UNS - CONICET 12 de Octubre 1842 - 8000 Bahía Blanca - Argentina
  2. Planta Piloto de Ingeniería Química - UNS - CONICET 12 de Octubre 1842 - 8000 Bahía Blanca - Argentina E-mail: ponzoni@criba.edu.ar msanchez@criba.edu.ar, dybrigno@criba.edu.ar

Keywords: graph theory, directed graphs, bipartite graphs, sparse matrices, block lower-triangular forms, assignment algorithms, partitioning algorithms.

 

Abstract

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.