Concurrent Implementation of Munkres Algorithm

Abstract

is minimized over all permutations II. For NA 5 N B , the naive (exhaustive search) complexity of the assignment problem is O[NB! / (NB N A ) ! ] . There are, however, a variety of exact solutions to the assignment problem with reduced complexity O[N;NB], (Refs.[l-31). Section 2 briefly describes one such method, Munkres Algorithm [2] , and presents a particular sequential implementation. Performance of the algorithm is examined for the particularly nasty problem of associating lists of random points within the unit square. In Section 3, the algorithm is generalized for concurrent execution, and performance results for runs on the Mark111 hypercube are presented. The input to the assignment problem is the matrix D Z E { d i j } of dissimilarities from Eq.(3). The first point to note is that the particular assignment which minimizes Eq.(6) is not altered if afixed value is added to or subtracted from all entries in any row or column of the cost matrix D. Exploiting this fact, Munkres solution to the Assignment Problem can be divided into two parts