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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, March 28, 2023, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Martin Fürer (Pennsylvania State University)

Most NP-hard graph problems can be solved efficiently when restricted to graphs of small width and provided with a corresponding tree decomposition. Thus, it is essential to find good tree decompositions efficiently. The goal is to approximate the width by a small constant factor and to have an efficient FPT (fixed parameter tractable) algorithm. FPT means that the time is O(f(k)g(n)) where k is the parameter (in this case the treewidth), n is the size of the input, f is a computable function and g is bounded by a polynomial. Korhonen’s [2021] new algorithm achieves a ratio of 2 with g linear. However, f remains a stumbling block for fast algorithms. Tree Decomposition (of width at most k) is NP-complete. Therefore, f(k) = O*(c^{k}), achieved by several algorithms, is theoretically satisfactory, but the base c is large. (O* omits polynomial factors.) This talk is about decreasing c. It starts with a quick review of the classical O*(4^{3k}) n^{2} algorithm of Robertson and Seymour [1995] and the 2^{O(k log k)} n log n improvement by Reed [1992]. Joint work with Mahdi Belbasi.

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