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Polynomial time approximation schemes for Euclidean TSP and other geometric problems

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1 Author(s)
Arora, S. ; Princeton Univ., NJ, USA

We present a polynomial time approximation scheme for Euclidean TSP in ℜ2. Given any n nodes in the plane and ε>0, the scheme finds a (1+ε)-approximation to the optimum traveling salesman tour in time n0(1/ε). When the nodes are in ℜd, the running time increases to n(O˜(logd-2n)/εd-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 lp for p⩾1 or other Minkowski norms)

Published in:

Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on

Date of Conference:

14-16 Oct 1996