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 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.
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ABSTRACT: Recently inJenkyns  andKorte/Hausmann  a tight worst-case bound for the well-known greedy heuristic for general independence systems has been deduced. Here some modifications of the greedy heuristic are investigated which allow to enlarge the current independent set by more than one element. It is shown that in spite of the additional enumeration incorporated in these heuristics they can behave worse than the usual greedy heuristic for some problem instances. For one of those modifications the same worst-case bound as mentioned above — but no better one — has been proved again. These results underline the predominant role of the usual greedy heuristic for general independence systems.Krzlich wurde inJenkyns  undKorte/Hausmann  eine scharfe Gtegarantie fr die bekannte Greedy-Heuristik fr allgemeine Unabhngigkeitssysteme hergeleitet. Hier werden nun einige Modifikationen der Greedy-Heuristik untersucht, die es gestatten, die laufende unabhngige Menge durch mehr als ein Element zu vergrern. Es wird gezeigt, da sich diese Heuristiken — trotz der zustzlich in sie eingebauten Enumeration — in Einzelfllen schlechter verhalten knnen als die gewhnliche Greedy-Heuristik.Fr eine dieser Modifikationen konnte wieder die gleiche Gtegarantie wie die oben erwhnte —aber keine bessere — bewiesen werden. Diese Ergebnisse unterstreichen die beherrschende Rolle der gewhnlichen Greedy-Heuristik fr allgemeine Unabhngigkeitssysteme.Mathematical Methods of Operational Research 11/1978; 22(1):219-228. · 0.31 Impact Factor
Conference Paper: A new algorithm for the generalized multidimensional assignment problem[Show abstract] [Hide abstract]
ABSTRACT: The authors present a fast near-optimal 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 multisensor-multitarget state estimation problem is that of data association-the problem of determining from which target, if any, a particular measurement originated. The data-association problem for tracking can be formulated as a generalized S -dimensional ( S -D) assignment problem. However, the problem is NP-hard for three or more sensor scans ( S ⩾3). An efficient and recursive generalized S -D assignment algorithm ( S ⩾3) suitable for near-optimal 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
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ABSTRACT: We investigate two geometric special cases of the three-dimensional assignment problem: Given are three sets B, R and G (blue, red and green) each containing n grid points in the Euclidean plane. We want to find a partition of B ∪ R ∪ G into n three0colored triangles such that (a) the total circumference of all triangles or (b) the total area of all triangles becomes minimum. Both versions of the problem are proved to be NP-hard.European Journal of Operational Research 02/1996; 91(3):611-618. · 2.04 Impact Factor