Summary: Polynomial Time Approximation Schemes for Euclidean TSP and other Geometric
Problems
Sanjeev Arora \Lambda
Princeton University
Abstract
We present a polynomial time approximation scheme for
Euclidean TSP in ! 2 . Given any n nodes in the plane
and ffl ? 0, the scheme finds a (1 + ffl)­approximation
to the optimum traveling salesman tour in time n O(1=ffl) .
When the nodes are in ! d , the running time increases to
n ”
O(log d\Gamma2 n)=ffl d\Gamma1
. The previous best approximation algo­
rithm 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, k­TSP,
Minimumdegree­k spanning tree, k­MST, etc. (This list may
get longer; our techniques are fairly general.) The previ­
ous best approximation algorithms for all these problems

Source: Arora, Sanjeev - Department of Computer Science, Princeton University

Collections: Computer Technologies and Information Sciences