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Abstract: . We present an additive characterization of Monge matrices based on the extremal rays of the cone of nonnegative Monge matrices. By using this characterization, a simple proof for an old result by Supnick (1957) on the traveling salesman problem on Monge matrices is derived. Keywords. Combinatorial optimization, traveling salesman problem, Monge matrix, cone. 1 Introduction An m \Theta n matrix C = (c ij ) is called a Monge matrix if it satisfies the Monge property c ij + c rs c is + c rj... (Update)
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BibTeX entry: (Update)
R. Rudolf and G.J. Woeginger, The Cone of Monge Matrices: Extremal Rays and Applications, ZOR 42, 1995, 161--168. http://citeseer.ist.psu.edu/rudolf94cone.html More
@misc{ rudolf95cone,
author = "R. Rudolf and G. Woeginger",
title = "The Cone of Monge Matrices: Extremal Rays and Applications",
text = "R. Rudolf and G.J. Woeginger, The Cone of Monge Matrices: Extremal Rays
and Applications, ZOR 42, 1995, 161--168.",
year = "1995",
url = "citeseer.ist.psu.edu/rudolf94cone.html" }
Citations (may not include all citations):193 The traveling salesman problem (context) - Lawler, Lenstra et al. - 1985
20 On simple linear programming problems (context) - Hoffman - 1961
19 Speed-up in dynamic programming (context) - Yao - 1982
11 vertex traveling salesman problem that can be solved in O (context) - Park, case et al. - 1991
10 M'emoires sur la th'eorie des d'eblais et des remblais (context) - Monge
8 Optimierung und Kontrolle (context) - Burkard, Klinz et al. - 1994
3 a class of polynomially solvable travelling salesman problem.. (context) - Michalski - 1987
1 Extremal hamiltonian lines (context) - Supnick - 1957
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