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Proceedings of 37th Conference on Foundations of Computer Science (1996)
Burlington, VT
Oct. 14, 1996 to Oct. 16, 1996
ISBN: 0-8186-7594-2
pp: 2
S. Arora , Princeton Univ., NJ, USA
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).
INDEX TERMS
computational geometry; polynomial time approximation; Euclidean TSP; geometric problems; optimum traveling salesman tour; Steiner Tree; Euclidean problems; k-TSP; Minimum degree-k; spanning tree; k-MST; best approximation
CITATION

S. Arora, "Polynomial time approximation schemes for Euclidean TSP and other geometric problems," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 2.
doi:10.1109/SFCS.1996.548458
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