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The Traveling Salesman Problem Under Squared Euclidean Distances
Abstract
International audienceLet be a set of points in , and let be a real number. We define the distance between two points as , where denotes the standard Euclidean distance between and . We denote the traveling salesman problem under this distance function by TSP(). We design a 5-approximation algorithm for TSP(2,2) and generalize this result to obtain an approximation factor of for and all . We also study the variant Rev-TSP of the problem where the traveling salesman is allowed to revisit points. We present a polynomial-time approximation scheme for Rev-TSP with , and we show that Rev-TSP is APX-hard if and . The APX-hardness proof carries over to TSP for the same parameter ranges- info:eu-repo/semantics/conferenceObject
- Conference papers
- Geometric traveling salesman problem
- power-assignment in wireless networks
- distance-power gradient
- NP-hard
- APX-hard
- ACM: G.: Mathematics of Computing/G.2: DISCRETE MATHEMATICS/G.2.2: Graph Theory
- ACM: F.: Theory of Computation/F.2: ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY/F.2.2: Nonnumerical Algorithms and Problems
- [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]
- [INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]