The cone of Monge matrices: Extremal rays and applications

@article{Rudolf1995TheCO,
  title={The cone of Monge matrices: Extremal rays and applications},
  author={R{\"u}diger Rudolf and Gerhard J. Woeginger},
  journal={Zeitschrift f{\"u}r Operations Research},
  year={1995},
  volume={42},
  pages={161-168}
}
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. 
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1 We constructively show that any cyclic Monge distance 2 matrix can be represented as the graph distances between 3 vertices on the outer face of a planar graph. The structure 4 of the planar graph
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This paper presents a survey on Monge matrices and related Monge properties and their role in combinatorial optimization, and deals with the following three main topics: fundamental combinatorsial properties of Monge structures, applications of MonGE properties to optimization problems and recognition ofMonge properties.
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