Minimum-weight perfect matching for non-intrinsic distances on the line
Consider a real line equipped with a (not necessarily intrinsic) distance. We deal with the minimum-weight perfect matching problem for a complete graph whose points are located on the line and whose edges have weights equal to distances along the line. This problem is closely related to one-dimensi...
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| creator | Delon, Julie Salomon, Julien Sobolevski, Andrei |
| description | Consider a real line equipped with a (not necessarily intrinsic) distance. We deal with the minimum-weight perfect matching problem for a complete graph whose points are located on the line and whose edges have weights equal to distances along the line. This problem is closely related to one-dimensional Monge-Kantorovich trasnport optimization. The main result of the present note is a "bottom-up" recursion relation for weights of partial minimum-weight matchings. |
| doi_str_mv | 10.48550/arxiv.1102.1558 |
| format | Article |
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| subjects | Graph theory Matching Mathematics - Optimization and Control Minimum weight Optimization |
| title | Minimum-weight perfect matching for non-intrinsic distances on the line |
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