Shorter tours by nicer ears: 7/5-approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs
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We prove new results for approximating the graph-TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees.
For the graph-TSP itself, we improve the approximation ratio to 7/5. For a generalization, the minimum T-tour problem, we obtain the first nontrivial approximation algorithm, with ratio 3/2. This contains the s-t-path graph-TSP as a special case. Our 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.
Mathematics Subject Classification (2000)90C27 05C85 68R10
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