Geodesic
Asymptotically optimal algorithm for finding one and two edge-disjoint traveling salesman routes of maximal weight in Euclidean space
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 2, pp. 23-32

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The paper presents a polynomial approximation algorithm $\mathcal A$ solving the problem of finding one and two edge-disjoint Hamiltonian cycles (traveling salesman routes) of maximal weight in a complete weighted undirected graph in multidimensional Euclidean space. The asymptotic optimality of the algorithm is established. 
@article{TIMM_2008_14_2_a3,
     author = {E. Kh. Gimadi},
     title = {Asymptotically optimal algorithm for finding one and two edge-disjoint traveling salesman routes of maximal weight in {Euclidean} space},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {23--32},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2008_14_2_a3/}
}
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E. Kh. Gimadi. Asymptotically optimal algorithm for finding one and two edge-disjoint traveling salesman routes of maximal weight in Euclidean space. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 2, pp. 23-32. http://geodesic.mathdoc.fr/item/TIMM_2008_14_2_a3/