Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, April 06, 2004, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Yoshio Okamoto

The traveling salesman problem with few inner points

We study the traveling salesman problem in the 2-dimensional Euclidean plane. The problem is NP-hard in general, but trivial if the points are in convex position. In this talk, we investigate the influence of the number of inner points (i.e., points in the interior of the convex hull) on the computational complexity of the problem. We give a simple algorithm for this problem which runs in time O(k!kn) and space O(n), when n is the total number of input points and k is the number of inner points. If k is taken as a parameter, this algorithm is fixed-parameter-tractable (FPT), and also implies that the problem can be solved in polynomial time if k=O(log n/log log n). We also consider some variants of the traveling salesman problem in this setting, and give FPT algorithms for them.

(This is a joint work with Michael Hoffmann)

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