Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

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

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Martin Fürer (Pennsylvania State University)

Finding tree decompositions

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) n² 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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