A FAST RECONFIGURABLE NETWORK FOR GRAPH CONNECTIVITY AND TRANSITIVE CLOSURE

Abstract

This paper presents a VLSI array for labeling the connected components of a graph on N nodes in O(r) steps using a reconfigurable bus of width m bits, such that [Formula: see text] and 1≤r≤m. The network architecture consists of an array of simple logic nodes which are connected by a reconfigurable bus. To solve a problem on N nodes, the array uses N processors and N(N−1)/2 switches. The proposed connectivity and transitive closure algorithms are based on a processor indexing scheme which employs constant-weight codes. It is shown that when r is a constant, then the algorithm takes O(1) time using a bus of width O(N1/r), and when r=[ log N/ loglog N], the algorithm takes O( log N/ loglog N) time using a bus of width O( log N) bits.