The traveling salesman problem with distances one and two
Mathematics of Operations Research
On sparse spanners of weighted graphs
Discrete & Computational Geometry
A polynomial-time approximation scheme for weighted planar graph TSP
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Light spanners and approximate TSP in weighted graphs with forbidden minors
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate TSP in Graphs with Forbidden Minors
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
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 contraction decomposition
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Contraction decomposition in h-minor-free graphs and algorithmic applications
Proceedings of the forty-third annual ACM symposium on Theory of computing
Approximation schemes for minimum 2-connected spanning subgraphs in weighted planar graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Minimum weight 2-edge-connected spanning subgraphs in planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Given an edge-weighted graph G and ε0, a (1+ε)-spanner is a spanning subgraph G′ whose shortest path distances approximate those of G within a factor of 1+ε. For G from certain graph families (such as bounded genus graphs and apex graphs), we know that light spanners exist. That is, we can compute a (1+ε)-spanner G′ with total edge weight at most a constant times the weight of a minimum spanning tree. This constant may depend on ε and the graph family, but not on the particular graph G nor on the edge weighting. The existence of light spanners is essential in the design of approximation schemes for the metric TSP (the traveling salesman problem) and similar graph-metric problems. In this paper we make some progress towards the conjecture that light spanners exist for every minor-closed graph family: we show that light spanners exist for graphs with bounded pathwidth, and they are computed by a greedy algorithm. We do this via the intermediate construction of light monotone spanning trees in such graphs.