Showing papers on "Las Vegas algorithm published in 1982"
01 Apr 1982
TL;DR: Two parallel algorithms to compute the determinant and characteristic polynomial of n×n-matrices and the gcd of polynomials of degree ≤n and a fast parallel Las Vegas algorithm for the rank of matrices are presented.
Abstract: We present parallel algorithms to compute the determinant and characteristic polynomial of n×n-matrices and the gcd of polynomials of degree ≤n. The algorithms use parallel time O(log2n) and a polynomial number of processors. We also give a fast parallel Las Vegas algorithm for the rank of matrices. All algorithms work over arbitrary fields.
233 citations
05 May 1982
TL;DR: Two polynomial time algorithms are described which test isomorphism of undirected graphs whose eigenvalues have bounded multiplicity, if X and Y are graphs of eigenvalue multiplicity m.
Abstract: We investigate the connection between the spectrum of a graph, i.e. the eigenvalues of the adjacency matrix, and the complexity of testing isomorphism. In particular we describe two polynomial time algorithms which test isomorphism of undirected graphs whose eigenvalues have bounded multiplicity. If X and Y are graphs of eigenvalue multiplicity m, then the isomorphism of X and Y can be tested by an O(n4m+c) deterministic and by an O(n2m+c) Las Vegas algorithm, where n is the number of vertices of X and Y.
196 citations