Constant Time Algorithms for Graph Connectivity Problems on Reconfigurable Meshes Using Fewer Processors

This paper makes an efficient improvement of processor complexity while solving some connectivity problems on a reconfigurable meshes. We first derive two constant time algorithms in the proposed parallel processing system for computing the dominators and the dominator tree of an undirected graph either using a 3-D n×n×n processors or a 2-D n2×n2 processors, where n is the number of vertices of the graph. Then based on the dominator tree algorithm, we also solve many other graph connectivity problems in a constant time. They are the articulation points, bridges, biconnected components, and bridge-connected components problem in undirected graphs.