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

Authors Eduard Eiben , Robert Ganian, Thekla Hamm, O-joung Kwon



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Author Details

Eduard Eiben
  • Department of Informatics, University of Bergen, Bergen, Norway
Robert Ganian
  • Vienna University of Technology, Vienna, Austria
Thekla Hamm
  • Vienna University of Technology, Vienna, Austria
O-joung Kwon
  • Department of Mathematics, Incheon National University, Korea

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Eduard Eiben, Robert Ganian, Thekla Hamm, and O-joung Kwon. Measuring what Matters: A Hybrid Approach to Dynamic Programming with Treewidth. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 42:1-42:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.MFCS.2019.42

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Parameterized complexity
  • treewidth
  • rank-width
  • fixed-parameter algorithms

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