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• W2110367141 abstract "We present a polynomial time approximation scheme for Euclidean TSP in /spl Rfr//sup 2/. Given any n nodes in the plane and /spl epsiv/>0, the scheme finds a (1+/spl epsiv/)-approximation to the optimum traveling salesman tour in time n/sup 0(1//spl epsiv/)/. When the nodes are in /spl Rfr//sup d/, the running time increases to n(O/spl tilde/(log/sup d-2/n)//spl epsiv//sup d-1/) The previous best approximation algorithm for the problem (due to Christofides (1976)) achieves a 3/2-approximation in polynomial time. We also give similar approximation schemes for a host of other Euclidean problems, including Steiner Tree, k-TSP, Minimum degree-k, spanning tree, k-MST, etc. (This list may get longer; our techniques are fairly general.) The previous best approximation algorithms for all these problems achieved a constant-factor approximation. All our algorithms also work, with almost no modification, when distance is measured using any geometric norm (such as l/sub p/ for p/spl ges/1 or other Minkowski norms)." @default.
• W2110367141 created "2016-06-24" @default.
• W2110367141 creator A5079951047 @default.
• W2110367141 date "2002-12-24" @default.
• W2110367141 modified "2023-10-03" @default.
• W2110367141 title "Polynomial time approximation schemes for Euclidean TSP and other geometric problems" @default.
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• W2110367141 doi "https://doi.org/10.1109/sfcs.1996.548458" @default.
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