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 language | English (US) |
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Pages (from-to) | 2-11 |
Number of pages | 10 |
Journal | Annual Symposium on Foundations of Computer Science - Proceedings |
State | Published - 1996 |
Event | Proceedings of the 1996 37th Annual Symposium on Foundations of Computer Science - Burlington, VT, USA Duration: Oct 14 1996 → Oct 16 1996 |
All Science Journal Classification (ASJC) codes
- Hardware and Architecture