Good triangulations yield good tours

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2009, Paris, France, June 2-4 2009

We present two approaches for the Euclidean TSP which compute high quality tours for large instances. Both approaches are based on pseudo backbones consisting of all common edges of good tours. The first approach starts with some pre-computed good tours. Using this approach we found record tours for seven VLSI instances. The second approach is window based and constructs from scratch very good ...

Effective Heuristics for Large Euclidean TSP Instances Based on Pseudo Backbones

We present two approaches for the Euclidean TSP which compute high quality tours for large instances. Both approaches are based on pseudo backbones consisting of all common edges of good tours. The first approach starts with some pre-computed good tours. Using this approach we found record tours for seven VLSI instances. The second approach is window based and constructs from scratch very good ...

Bounds on the maximum multiplicity of some common geometric graphs

We obtain new lower and upper bounds for the maximum multiplicity of some weighted, and respectively non-weighted, common geometric graphs drawn on n points in the plane in general position (with no three points collinear): perfect matchings, spanning trees, spanning cycles (tours), and triangulations. (i) We present a new lower bound construction for the maximum number of triangulations a set ...

Good Triangulations in Plane

Chromatic Statistics for Triangulations and Fuß-Catalan Complexes

We introduce Fuß–Catalan complexes as d-dimensional generalisations of triangulations of a convex polygon. These complexes are used to refine Catalan numbers and Fuß–Catalan numbers, by introducing colour statistics for triangulations and Fuß–Catalan complexes. Our refinements consist in showing that the number of triangulations, respectively of Fuß–Catalan complexes, with a given colour distri...