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- W28955333 abstract "In this chapter we use the permutation definition of TSP introduced in Chapter 1. Given a cost matrix C of size n, the Traveling Salesman Problem (TSP) is thus to find a tour γ on N = {1, 2,..., n} such that c(γ) = ∑ i∈N c i,γ(i) is minimum. We allow some non-diagonal elements of C to be ∞. For E = {(i,j): c ij is finite}, G = (N, E) is called the digraph associated with C and we call C compatible with G. If C is symmetric, then we define G as an undirected graph. As in previous chapters, TSP can be equivalently stated as the problem of finding a tour H in G such that % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfKttLearuqr1ngBPrgarmqr1ngBPrgitL % xBI9gBamXvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2D % aeHbuLwBLnhiov2DGi1BTfMBaebbfv3ySLgzGueE0jxyaibaieYlf9 % irVeeu0dXdh9vqqj-hEeeu0xXdbba9frFj0-OqFfea0dXdd9vqaq-J % frVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabi % GaciaacaqabeaadaabauaaaOqaaiabdogaJnaabmaabaWefv3ySLgz % nfgDOfdarCqr1ngBPrginfgDObYtUvgaiyaacqWFlecsaiaawIcaca % GLPaaacqGH9aqpdaaeabqaamaaBaaaleaadaqadaqaaiabdMgaPjab % cYcaSiabdQgaQbGaayjkaiaawMcaaiabgIGiolab-Tqiibqabaaabe % qab0GaeyyeIuoakiabdogaJnaaBaaaleaacqWGPbqAcqWGQbGAaeqa % aaaa!5B69! $$ cleft( mathcal{H} right) = sum {_{left( {i,j} right) in mathcal{H}} } c_{ij} $$ is minimum. We denote this problem by TSP(G, C). When G is a complete digraph or graph (or equivalently, all the non-diagonal entries of C are finite), we denote the problem by TSP(C)" @default.
- W28955333 created "2016-06-24" @default.
- W28955333 creator A5016690675 @default.
- W28955333 date "2007-01-01" @default.
- W28955333 modified "2023-09-27" @default.
- W28955333 title "Polynomially Solvable Cases of the TSP" @default.
- W28955333 doi "https://doi.org/10.1007/0-306-48213-4_11" @default.
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