QuickMatch : A Very Fast Algorithm for the Assignment Problem

In this paper, we consider the linear assignment problem defined on a bipartite network G = (r U I, A). The problem may be described as assigning each person in a set UT to a set V of tasks so as to minimize the total cost of the assignment. The cost of assigning person i to task j is ci if (i, j) E A and is infinite otherwise. This paper describes a new algorithm called QuickMiatch for solving the assignment problem. QuickMatch is based on the successive shortest path (SSP) algorithm for the assignment problem, which in turn is a modification of Kuhn's primal dual algorithm. However, we have added several natural heuristics that speed up the performance of the standard successive shortest path algorithm by several orders of magnitude. We present some theoretical justifications as to why the algorithm's performance is superior in practice to the usual SSP algorithm, and we provide computational support as well. In addition, the theoretical analysis and computational testing supports (but does not prove) the hypothesis that QuickMatch runs in linear tiie (i.e., in expected time 0(n)) on randomly generated sparse assignment problems.