Greedy and Greedy Algorithms for Multidimensional Data Association
ABSTRACT 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 NPhard 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 semigreedy approach introduced in earlier research. Experimental results on the accuracy and speed of the proposed algorithms in MTT problems are provided.
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Conference Paper: A new algorithm for the generalized multidimensional assignment problem
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ABSTRACT: The authors present a fast nearoptimal assignment algorithm to solve the generalized multidimensional assignment problem. Such problems arise in surveillance and tracking systems estimating the states of an unknown number of targets. The central problem in a multisensormultitarget state estimation problem is that of data associationthe problem of determining from which target, if any, a particular measurement originated. The dataassociation problem for tracking can be formulated as a generalized S dimensional ( S D) assignment problem. However, the problem is NPhard for three or more sensor scans ( S ⩾3). An efficient and recursive generalized S D assignment algorithm ( S ⩾3) suitable for nearoptimal track initiation of targets with ballistic trajectories in polynomial time is given. Complete algorithmic details and preliminary simulation results are presentedSystems, Man and Cybernetics, 1992., IEEE International Conference on; 11/1992 

Chapter: Approximation Algorithms
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ABSTRACT: Most interesting realworld optimization problems are very challenging from a computational point of view. In fact, quite often, finding an optimal or even a nearoptimal solution to a largescale optimization problem may require computational resources far beyond what is practically available. There is a substantial body of literature exploring the computational properties of optimization problems by considering how the computational demands of a solution method grow with the size of the problem instance to be solved (see e.g. Chapter 11 or Aho et al., 1979). A key distinction is made between problems that require computational resources that grow polynomially with problem size versus those for which the required resources grow exponentially. The former category of problems are called efficiently solvable, whereas problems in the latter category are deemed intractable because the exponential growth in required computational resources renders all but the smallest instances of such problems unsolvable.03/2006: pages 557585;