Achieving optimality for gate matrix layout and PLA folding: a graph theoretic approach

Abstract

We present O( n 3) heuristic algorithms for multiple/ simple PLA folding, which also apply to the matrix layout problem. Our heuristic is based on a new approach, where both problems are shown to be composed by a permutation step followed by a compaction step. Therefore we are able to show that the exponential complexity of the problem stems from the permutation step—where a good configuration is searched—, since the compaction step—where the actual folding takes place—is optimally solved in polynomial time. We discuss bounds on the distance of the obtained solution to the optimal and give sufficient conditions for the solution to be optimal. Verification of the sufficient conditions constitutes part of the proposed algorithms, and is in fact used to construct the heuristic solution. An example showing the multiple folding of a 58 × 19 PLA produced by the proposed algorithm is presented.