Minimum spanning tree on the HMESH architecture

A fast algorithm to compute the minimum spanning tree of a given undirected graph on a hierarchical mesh-connected computer (HMESH) is presented. The time complexity of the algorithm is O(log² n), where n is the number of nodes in the graph. HMESH is a broadcast bus VLSI architecture which consists of n× n processing elements (PEs) in a mesh-connected structure and a hierarchy of broadcast buses in each row and column of the mesh structure such that each broadcast bus is connected to exactly k PE´s, where k is a small constant. It is shown that with simple modifications to the algorithm, the MST of an n node graph can be found on a HMESH of size p×p in O[n/p]² log n log p) time. It is also shown how to compute connected components and transitive closure of a given undirected graph in O(log² n) with a few modifications to the algorithm presented for computing the minimum spanning tree