Geodesic
Minimum-weight perfect matching for non-intrinsic distances on the line
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XX, Tome 390 (2011), pp. 52-68

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We consider a minimum-weight perfect matching problem on the line and establish a “bottom-up” recursion relation for weights of partial minimum-weight matchings. 
@article{ZNSL_2011_390_a1,
     author = {J. Delon and J. Salomon and A. Sobolevski},
     title = {Minimum-weight perfect matching for non-intrinsic distances on the line},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {52--68},
     publisher = {mathdoc},
     volume = {390},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_390_a1/}
}
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J. Delon; J. Salomon; A. Sobolevski. Minimum-weight perfect matching for non-intrinsic distances on the line. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XX, Tome 390 (2011), pp. 52-68. http://geodesic.mathdoc.fr/item/ZNSL_2011_390_a1/