Shorter Tours by Nicer Ears: 7/5-approximation for graphic TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs
Abstract
We prove new results for approximating the graphic TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees. For the graphic TSP itself, we improve the approximation ratio to 7/5. For a generalization, the connected--join problem, we obtain the first nontrivial approximation algorithm, with ratio 3/2. This contains the graphic --path-TSP as a special case. Our improved approximation guarantee for finding a smallest 2-edge-connected spanning subgraph is 4/3. The key new ingredient of all our algorithms is a special kind of ear-decomposition optimized using forest representations of hypergraphs. The same methods also provide the lower bounds (arising from LP relaxations) that we use to deduce the approximation ratios.
Keywords
Cite
@article{arxiv.1201.1870,
title = {Shorter Tours by Nicer Ears: 7/5-approximation for graphic TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs},
author = {András Sebő and Jens Vygen},
journal= {arXiv preprint arXiv:1201.1870},
year = {2012}
}