Research and Advances

Cellular arrays for the solution of graph problems


A cellular array is a two-dimensional, checkerboard type interconnection of identical modules (or cells), where each cell contains a few bits of memory and a small amount of combinational logic, and communicates mainly with its immediate neighbors in the array. The chief computational advantage offered by cellular arrays is the improvement in speed achieved by virtue of the possibilities for parallel processing. In this paper it is shown that cellular arrays are inherently well suited for the solution of many graph problems. For example, the adjacency matrix of a graph is easily mapped onto an array; each matrix element is stored in one cell of the array, and typical row and column operations are readily implemented by simple cell logic. A major challenge in the effective use of cellular arrays for the solution of graph problems is the determination of algorithms that exploit the possibilities for parallelism, especially for problems whose solutions appear to be inherently serial. In particular, several parallelized algorithms are presented for the solution of certain spanning tree, distance, and path problems, with direct applications to wire routing, PERT chart analysis, and the analysis of many types of networks. These algorithms exhibit a computation time that in many cases grows at a rate not exceeding log2 n, where n is the number of nodes in the graph. Straightforward cellular implementations of the well-known serial algorithms for these problems require about n steps, and noncellular implementations require from n2 to n3 steps.

View this article in the ACM Digital Library.

Join the Discussion (0)

Become a Member or Sign In to Post a Comment

The Latest from CACM

Shape the Future of Computing

ACM encourages its members to take a direct hand in shaping the future of the association. There are more ways than ever to get involved.

Get Involved

Communications of the ACM (CACM) is now a fully Open Access publication.

By opening CACM to the world, we hope to increase engagement among the broader computer science community and encourage non-members to discover the rich resources ACM has to offer.

Learn More