Solving Physical Design Problems on a Vector Machine

Abstract

In this paper, we describe parallel algorithms for two physical design problems. The target machine is the Alliant FX/80, which is a shared-memory multiprocessor with up to 8 advanced computational elements which are individually capable of vector operation. First, we describe the parallel implementation of an r-dimensional circuit placement algorithm. The objective of the placement problem is to arrange n logic blocks in an r-dimensional space so as to minimize the length of the interconnect wiring among the blocks. The problem is known to be NP-complete, and the numerical optimization technique presented in this paper finds a local optimum solution. Next, we discuss a parallel version of Kernighan and Lin's algorithm for the two-way circuit partition problem. Given n logic blocks and their connectivity matrix C, the problem is to generate a balanced two-way partition of the blocks such that the wiring across the partition is minimum. The partition problem is NPcomplete, but the Kernighan-Lin heuristic algorithm generates a near-optimal solution.