Matching, Euler tours and the Chinese postman
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The solution of the Chinese postman problem using matching theory is given. The convex hull of integer solutions is described as a linear programming polyhedron. This polyhedron is used to show that a good algorithm gives an optimum solution. The algorithm is a specialization of the more generalb-matching blossom algorithm. Algorithms for finding Euler tours and related problems are also discussed.
- van Aardenne-Ehrenfest and N.G. de Bruijn, “Circuits and trees in oriented graphs”,Simon Stevin 28 (1951) 203–217.
- E.J. Beltrami and L.D. Bodin, “Networks and vehicle routing for municipal waste collection”, Report No. UPS 72-18, State University of New York, Stony Brook, N.Y. (1972).
- C. Berge,The theory of graphs and its applications (Wiley, New York, 1962).
- J. Edmonds, “Paths, trees and flowers”,Canadian Journal of Mathematics 17 (1965) 449–467.
- J. Edmonds, “Maximum matching and a polyhedron with 0, 1-vertices”,Journal of Research of the National Bureau of Standards Section B, 1, 2 (1965) 125–130.
- J. Edmonds, “The Chinese postman problem”,Operations Research 13 Suppl. 1 (1965) 373.
- J. Edmonds and E.L. Johnson, “Matching: a well-solved class of integer linear programs”, in:Combinatorial structures and their applications (Gordon and Breach, New York, 1970) 89–92.
- J. Edmonds, E.L. Johnson and S. Lockhart, “Blossom I: a computer code for the matching problem”, to appear.
- L. Euler, “Solutio problematis ad geometriam situs pertinentis”,Commentarii Academiae Petropolitanae 8 (1736) 128–140.
- L.R. Ford Jr. and D.R. Fulkerson,Flows in networks (Princeton Univ. Press, Princeton, N.J., 1962).
- A.J. Hoffman, “Some recent applications of the theory of linear inequalities to extremal combinatorial analysis”, in:Proceedings of Symposia on Applied Mathematics Vol. 10 (American Mathematical Society, Providence, R.I., 1960).
- T.C. Hu, “Revised matrix algorithms for shortest paths in a network“,SIAM Journal 15 (1967) 207–218.
- T.M. Liebling,Graphentheorie in Planungs- und Tourenproblemen, Lecture Notes in Operations Research and Mathematical Systems 21 (Springer, Berlin, 1970).
- K. Mei-Ko, “Graphic programming using odd or even points”,Chinese Mathematics 1 (1962) 273–277.
- C.S. Orloff, “Routing and scheduling a fleet of vehicles to/from central facilities — the school bus problem”, Ph. D. Thesis, Cornell University, Ithaca, N.Y. (1972).
- R. Stricker, “Public sector vehicle routing: the Chinese postman problem”, Master Thesis, Massachusetts Institute of Technology, Cambridge, Mass. (August 1970).
- Matching, Euler tours and the Chinese postman
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