Permutation of sparse matrices to a specific lower block triangular form using graph decompositions

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–Karp's algorithm is employed to match the vertices, this classification being carried out by means of a modification of Dulmage–Mendelsohn's technique, which was devised by the authors. The second step is the application of Tarjan's algorithm to the square blocks obtained as a result of the first stage.