Tree-Based Algorithms for the Multidimensional Assignment Problem

The Multidimensional Assignment Problem (MAP) is an extension of the two-dimensional assignment problem in which we wish to find an optimal matching of elements between mutually exclusive sets. Although the two-dimensional assignment problem has been shown to be solvable in polynomial time, extending the dimensions to three makes the problem NP-complete. The multidimensional assignment problem has many practical applications including the data association problem.

[1]  Lang Hong,et al.  A genetic algorithm based multi-dimensional data association algorithm for multi-sensor--multi-target tracking , 1997 .

[2]  P. Pardalos,et al.  Handbook of Combinatorial Optimization , 1998 .

[3]  Thomas M. Liebling,et al.  Tracking elementary particles near their primary vertex: A combinatorial approach , 1996, J. Glob. Optim..

[4]  Kenneth C. Gilbert,et al.  MULTIDIMENSIONAL ASSIGNMENT PROBLEMS , 1988 .

[5]  Frits C. R. Spieksma,et al.  Multi index assignment problems: complexity, approximation, applications , 2000 .

[6]  William P. Pierskalla,et al.  Letter to the Editor - The Multidimensional Assignment Problem , 1968, Oper. Res..

[7]  Egon Balas,et al.  An Algorithm for the Three-Index Assignment Problem , 1991, Oper. Res..

[8]  Panos M. Pardalos,et al.  A Parallel Grasp for the Data Association Multidimensional Assignment Problem , 1999 .

[9]  Frits C. R. Spieksma,et al.  An LP-based algorithm for the data association problem in multitarget tracking , 2003, Comput. Oper. Res..

[10]  Ellis Horowitz,et al.  Fundamentals of data structures in C , 1976 .

[11]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[12]  Alan Frieze,et al.  An Algorithm for Solving 3-Dimensional Assignment Problems with Application to Scheduling a Teaching Practice , 1981 .

[13]  James Llinas,et al.  An introduction to multisensor data fusion , 1997, Proc. IEEE.

[14]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Search Procedures , 1995, J. Glob. Optim..

[15]  Jean-Francois Pusztaszeri,et al.  The Nonlinear Assignment Problem in Experimental High Energy Physics , 2000 .

[16]  Raymond E. Miller,et al.  Complexity of Computer Computations , 1972 .

[17]  Aubrey B. Poore,et al.  A Numerical Study of Some Data Association Problems Arising in Multitarget Tracking , 1994 .

[18]  H. Kuhn.  The Hungarian method for the assignment problem , 1955 .

[19]  Rainer E. Burkard,et al.  Linear Assignment Problems and Extensions , 1999, Handbook of Combinatorial Optimization.

[20]  Ellis Horowitz,et al.  Fundamentals of Data Structures , 1984 .

[21]  Jean-François Pusztaszeri.  Combinatorial algorithms for pattern recognition in composite tracking chambers , 1996 .

[22]  Celso C. Ribeiro,et al.  Greedy Randomized Adaptive Search Procedures , 2003, Handbook of Metaheuristics.