A survey of heuristics for the weighted matching problem

This survey paper reviews results on heuristics for two weighted matching problems: matchings where the vertices are points in the plane and weights are Euclidean distances, and the assignment problem. Several heuristics are described in detail and results are given for worst-case ratio bounds, absolute bounds, and expected bounds. Applications to practical problems and some mathematical complements are also included.

[1]  Jon Louis Bentley,et al.  Decomposable Searching Problems I: Static-to-Dynamic Transformation , 1980, J. Algorithms.

[2]  Jerome M. Kurtzberg,et al.  On Approximation Methods for the Assignment Problem , 1962, JACM.

[3]  D. Avis.  Worst case bounds for the Euclidean matching problem , 1981 .

[4]  Nicos Christofides.  Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem , 1976, Operations Research Forum.

[5]  Luc Devroye,et al.  An analysis of a decomposition heuristic for the assignment problem , 1985 .

[6]  Kazuo Murota,et al.  Linear-Time Approximation Algorithms for Finding the Minimum-Weight Perfect Matching on a Plane , 1981, Inf. Process. Lett..

[7]  Edward M. Reingold,et al.  Heuristics for weighted perfect matching , 1980, STOC '80.

[8]  Edward M. Reingold,et al.  Probabilistic analysis of divide-and-conquer heuristics for minimum weighted euclidean matching , 1983, Networks.

[9]  Robert E. Tarjan,et al.  On a Greedy Heuristic for Complete Matching , 1981, SIAM J. Comput..

[10]  David W. Walkup,et al.  Matchings in random regular bipartite digraphs , 1980, Discret. Math..

[11]  J. Beardwood,et al.  The shortest path through many points , 1959, Mathematical Proceedings of the Cambridge Philosophical Society.

[12]  J. Steele.  Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability , 1981 .

[13]  W. Donath.  Algorithm and average-value bounds for assignment problems , 1969 .

[14]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[15]  Edward M. Reingold,et al.  Divide and Conquer Heuristics for Minimum Weighted Euclidean Matching , 1983, SIAM J. Comput..

[16]  Edward M. Reingold,et al.  The Travelling Salesman Problem and Minimum Matching in the Unit Square , 1983, SIAM J. Comput..

[17]  Kazuo Murota,et al.  Heuristics for planar minimum-weight perfect metchings , 1983, Networks.

[18]  David W. Walkup,et al.  On the Expected Value of a Random Assignment Problem , 1979, SIAM J. Comput..

[19]  J. Edmonds.  Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.