Given as input an edge-weighted graph, we analyze two algorithms for finding subgraphs with low total edge weight. The first algorithm finds a separator subgraph with a small number of components, and is analyzed for graphs with an arbitrary excluded minor. The second algorithm finds a spanner with small stretch factor, and is analyzed for graphs in a hereditary family G(k). These results imply (i) a QPTAS (quasi-polynomial time approximation scheme) for the TSP (traveling salesperson problem) in unweighted graphs with an excluded minor, and (ii) a QPTAS for the TSP in weighted graphs with bounded genus.
CITATION STYLE
Grigni, M. (2000). Approximate TSP in graphs with forbidden minors. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1853, pp. 869–877). Springer Verlag. https://doi.org/10.1007/3-540-45022-x_73
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