NCUBE/trademark/ implementation of some heuristics and an optimal algorithm for large-scale assignment problems

In order to solve some Fire Control Problems, we consider the standard assignment problem: Minimize z = ..sigma../sub i/ ..sigma../sub j/ c(ij) x(ij), subject to ..sigma../sub i/ x(ij) = ..sigma../sub j/ x(ij) = 1, with 1 less than or equal to i less than or equal to n, 1 less than or equal to j less than or equal to m, and x(ij) element of /l brace/0,1/r brace/. We are specially interested in large scale problems such that n and m greater than or equal to 100. We compare heuristics based on the Least Cost Rule and Vogel's Approximation Method, and the Hungarian Method. Our study focuses on the parallel implementation strategies on hypercube concurrent computers and on the solution optimality given the computational load. We describe implementations on an NCUBE (Beaverton, OR) hypercube. We also introduce scenarios which use a combination of different heuristics in order to get as fast as possible sub-optimal solutions. 5 refs., 4 figs.