A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
The traveling salesman problem with distances one and two
Mathematics of Operations Research
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
A polynomial-time approximation scheme for weighted planar graph TSP
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
An approximation scheme for planar graph TSP
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A linear-time approximation scheme for planar weighted TSP
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximation Algorithms via Structural Results for Apex-Minor-Free Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Light spanners in bounded pathwidth graphs
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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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.