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A polynomial algorithm for a constrained traveling salesman problem. (English) Zbl 0990.90102

Summary: We give a polynomial-time algorithm for finding a solution to the Traveling Salesman Problem when the points given are constrained to lie on a fixed set of smooth curves of finite length.

MSC:

90C27 Combinatorial optimization
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
Full Text: DOI

References:

[1] Nearly linear time approximation schemes for Euclidean TSP and other geometric problems. Proc 38th Ann Symp on Foundations of Computer Science, 1997.
[2] Cutler, Networks 10 pp 183– (1980) · Zbl 0442.90094 · doi:10.1002/net.3230100302
[3] De?ineko, Inf Process Lett 51 pp 141– (1994) · Zbl 0806.90121 · doi:10.1016/0020-0190(94)00071-9
[4] De?ineko, Inf Process Lett 59 pp 295– (1996) · Zbl 0900.68326 · doi:10.1016/0020-0190(96)00125-1
[5] and Computers and intractability, A guide to the theory of NP-completeness, Freeman, San Francisco, 1979.
[6] and ?Computational complexity,? The travelling salesman problem, et al. (Editors), Wiley, Chichester, 1985, Chapter 4.
[7] and (Editors), The travelling salesman problem, Wiley, Chichester, 1985.
[8] and Approximating geometrical graphs via ?spanners? and ?banyans?, STOC ’98, ACM, New York, 1999, pp. 540-550. · Zbl 1027.68651
[9] Rote, Networks 22 pp 91– (1992) · Zbl 0783.90118 · doi:10.1002/net.3230220106
[10] Rubinstein, SIAM J Discr Math 10 pp 1– (1997) · Zbl 0869.05023 · doi:10.1137/S0895480192241190
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