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arXiv · 1908.10132

Measuring what Matters: A Hybrid Approach to Dynamic Programming with Treewidth

Eduard Eiben·Robert Ganian·Thekla Hamm·O-joung Kwon
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Abstract

We develop a framework for applying treewidth-based dynamic programming on graphs with "hybrid structure", i.e., with parts that may not have small treewidth but instead possess other structural properties. Informally, this is achieved by defining a refinement of treewidth which only considers parts of the graph that do not belong to a pre-specified tractable graph class. Our approach allows us to not only generalize existing fixed-parameter algorithms exploiting treewidth, but also fixed-parameter algorithms which use the size of a modulator as their parameter. As the flagship application of our framework, we obtain a parameter that combines treewidth and rank-width to obtain fixed-parameter algorithms for Chromatic Number, Hamiltonian Cycle, and Max-Cut.

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Eduard Eiben, Robert Ganian, Thekla Hamm, O-joung Kwon. 2019-08-27. Measuring what Matters: A Hybrid Approach to Dynamic Programming with Treewidth. https://arxiv.org/abs/1908.10132

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