THE TRANSITIVE CLOSURE AND RELATED ALGORITHMS OF DIGRAPH ON THE RECONFIGURABLE ARCHITECTURE

Abstract

The reconfigurable architecture is a parallel computation model that consists of many processor elements (PEs) and a reconfigurable bus system. There are many variant proposed reconfigurable architectures, for example, reconfigurable mesh (R-Mesh), directional reconfigurable mesh (DR-Mesh), processor arrays with reconfigurable bus systems (PARBS), complete directional processor arrays with reconfigurable bus systems (CD-PARBS), reconfigurable multiple bus machine (RMBM), directional reconfigurable multiple bus machine (directional RMBM), and etc. In this paper, a transitive closure (TC) algorithm of digraph is proposed on the models without the directional capability (non-directional). Some related digraph problems, such as strongly connected digraph, strongly connected component (SCC), cyclic checking, and tree construction, can also be resolved by modifying our transitive closure algorithm. All the proposed algorithms are designed on a three-dimensional (3-D) n×n×n non-directional reconfigurable mesh, n is the number of vertices in a digraph D, and can resolve the respective problems in O(log d(D)) time, d(D) is the diameter of the digraph D. The cyclic checking problem can be further reduced to O(log c(D)) time, c(D) is the minimum distance of cycles in the digraph D. There exist two different approaches: the matrix multiplication approach on the non-directional models for algebraic path problems (APP) and s-t connectivity approach on the directional models. In this paper, we will use the tree construction algorithm to prove those two approaches are insufficient to resolve all digraph problems and demonstrate why our approach is so important and innovative for digraph problems on the reconfigurable models.