An Efficient Approximation of the Traveling Salesman Polytope Using Lifting Methods
Combinatorics
2007-05-23 v1 Metric Geometry
Abstract
For the Traveling Salesman Polytope on n cities T_n, we construct its approximation Q_k, k=1, 2, . . ., n^(1/3) using a projection of a polytope whose number of facets is polynomial in n (of degree linear in k). We show that T_n is contained in Q_k for each k, and that the scaling of Q_k by k/n+O(1/n) is contained in T_n for each k. We show that certain facets of T_n lie on the boundary of Q_k.
Keywords
Cite
@article{arxiv.math/0610385,
title = {An Efficient Approximation of the Traveling Salesman Polytope Using Lifting Methods},
author = {Ellen Veomett},
journal= {arXiv preprint arXiv:math/0610385},
year = {2007}
}
Comments
26 pages