Don't be Greedy, be Neighborly, a new assignment algorithm

Abstract

This paper proposes a new algorithm, the Neighborly algorithm, for solving the assignment problem. The new algorithm achieves much better results than the Greedy algorithm while still running in order N log2 (N). The most efficient algorithm to optimally solve the assignment problem, the JVC algorithm, requires order $\mathbf{N}^{\wedge}3$ operations. However, the Greedy algorithm is still in wide use today by target tracking algorithm practitioners due to its speed. The biggest problem with the Greedy algorithm is that the algorithm makes irrevocable, short sighted, assignments without regard to the global optimal solution. To overcome this weakness the Greedy algorithm is modified by incorporating some of the steps used by the Auction algorithm. To the author's knowledge, no new sub-optimal algorithms for solving the assignment problem have been proposed in recent years. Simulation results for the Neighborly algorithm compare favorably to optimal algorithms in the sparse target environment, but perform poorly, as expected, in very dense target environments. In both sparse and dense target environments, the Neighborly algorithm outperforms the Greedy algorithm in both computational efficiency and assignment results.