Greedy and $K$-Greedy Algorithms for Multidimensional Data Association

The multidimensional assignment (MDA) problem is a combinatorial optimization problem arising in many applications, for instance multitarget tracking (MTT). The objective of an MDA problem of dimension
d
∈
N
is to match groups of
d
objects in such a way that each measurement is associated with at most one track and each track is associated with at most one measurement from each list, optimizing a certain objective function. It is well known that the MDA problem is NP-hard for
d
≥ 3. In this paper five new polynomial time heuristics to solve the MDA problem arising in MTT are presented. They are all based on the semi-greedy approach introduced in earlier research. Experimental results on the accuracy and speed of the proposed algorithms in MTT problems are provided.