Polynomial time approximation schemes for Euclidean TSP and other geometric problems

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Abstract

We present a polynomial time approximation scheme for Euclidean TSP in R2. Given any n nodes in the plane and ε>O, the scheme finds a (1+ε)-approximation to the optimum traveling salesman tour in time nO(1/ε). When the nodes are in Rd, the running time increases to nO(log(d-2)n)/ε(d-1). The previous best approximation algorithm for the problem (due to Christofides) 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 lp for p≥1 or other Minkowski norms).

Original languageEnglish (US)
Pages (from-to)2-11
Number of pages10
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - Dec 1 1996

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture

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