Polynomial time approximation schemes for Euclidean TSP and other geometric problems
We present a polynomial time approximation scheme for Euclidean TSP in {Re}{sup 2}. Given any n nodes in the plane anti {epsilon} > 0, the scheme finds a (1 + {epsilon})-approximation to the optimum traveling salesman tour in time n{sup O(1/{epsilon})}. When the nodes are in {Re}{sup d}, the running time increases to n{sup O}(log{sup d-2} n)/{epsilon}{sup 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 {ell}{sub p} for p {ge} 1 or other Minkowski norms).
- OSTI ID:
- 457631
- Report Number(s):
- CONF-961004--
- Country of Publication:
- United States
- Language:
- English
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