Showing papers by "Alberto Sangiovanni-Vincentelli published in 1977"

An efficient heuristic cluster algorithm for tearing large-scale networks

Abstract: An efficient heuristic algorithm for solving a cluster problem associated with the tearing of an undirected graph is presented via the concept of a contour tableau. The required computation time is shown to be bounded by \theta (nb) , where n and b are the number of nodes and branches of the input graph, respectively. Experimental results show that our algorithm is highly efficient and yields near optimal solutions.

A graph theoretical interpretation of nonsymmetric permutation on sparse matrices

Abstract: In the tableau approach to large-electrical-network analysis, as well as in structure analysis, the finite-element method, linear programming etc., a very sparse linear algebraic set of equations Ax = b has to be solved repeatedly. To efficiently solve the system via Gaussian elimination, an optimization problem has to be faced: the selection of a pivot strategy to maintain the sparsity of the matrix A. It is possible also to follow a different strategy to fully exploit the sparsity of A, i.e. to transform A into an equivalent but more convenient form. Both of these problems have been studied and partially solved by means of directed graphs associated with A when symmetric permutations on A are allowed. In this paper, a graph theoretical interpretation has been given to nonsymmetric permutations on A, which can be considered a fundamental step towards the solution of the above-mentioned optimization problems. This interpretation is obtained through decomposition theorems on nonsymmetric permutations, correspondence theorems between column (row) permutations and topological operations on a directed graph representing A.