Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, October 13, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Heidi Gebauer

The Traveling Salesman Problem in Bounded Degree Graphs

The Traveling Salesman Problem (TSP) is one of the most fundamental NP-hard problems. The best known algorithm is the classical dynamic programming solution from 1962, discovered by Bellman, and, independently, by Held and Karp. It runs in time within a polynomial factor of 2^n where n is the number of cities. It is still open whether TSP in this general form can be solved in time O(1.999^n). For graphs of small degree (i.e. 3 or 4), though, some faster algorithms are known. But for the case where the degree bound, k, is at least 5, not much has been known so far. Björklund, Husfeldt, Kaski and Koivisto showed that TSP can be solved in (2 - epsilon)^n where epsilon is a constant depending on k only. They slightly modified the dynamic programming algorithm of Held and Karp and applied a lemma of Shearer which actually is about entropy.

Andreas Björklund, Thore Husfeldt, Petteri Kaski, Mikko Koivisto: The Travelling Salesman Problem in Bounded Degree Graphs. Proc. 35th International Colloquium on Automata, Languages, and Programming (ICALP), Part I. Lecture Notes in Computer Science 5125, (2008), 198-209 .

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