A new class of Heuristic Polynomial Time Algorithms to solve the Multidimensional Assignment Problem

The multidimensional assignment problem (MAP) is a combinatorial optimization problem arising in many applications, for instance in multi-target multi-sensor tracking problems. It is well-known that the MAP is NP-hard. The objective of a MAP is to match d-tuples of objects in such a way that the solution with the optimum total cost is found. In this paper a new class of approximation algorithms to solve the MAP is presented, named K-SGTS, and its effectiveness in multi-target multi-sensor tracking situations is shown. Its computational complexity is proven to be polynomial. Experimental results on the accuracy and speed of K-SGTS are provided in the last section of the paper