VLSI Algorithms for Finding a Fundamental Set of Cycles and aFundamental Set of

We present VLSI algorithms that run in O(n 2) steps for nding (and reporting) a fundamental set of cycles and a fundamental set of cutsets of an undirected graph on an nxn mesh of processors (SIMD). Both algorithms are decomposable and run in O(n 4 =k 2) steps for a graph with n vertices when the size of the mesh-connected computer is kxk and k < n. An idea similar to the one used in nding a fundamental set of cycles of an undirected graph yields an O(n 2) algorithm for generating shortest paths between all pairs of vertices of a graph on the same model.