Scaling and Optimization for List-Matching

Abstract

The list-matching problem is concerned with assigning N agents to N tasks in such a way that each task is assinged to precisely one agent. With each assignment σ there is associated the cost C ₁(σ) of performing the tasks. The goal is to choose σ which minimizes the cost. As N increases the problem becomes increasingly complex. The time required to solve it grows polynomially with N. The situation is quite similar to the one in the travelling salesman problem (TSP), although the time required to solve the TSP grows exponentially with N; the TSP is NP-complete. This complexity has motivated Hopfield and Tank [1] to devise a neural network computational approach to the TSP.