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Contraction-Bidimensionality of Geometric Intersection Graphs

Authors Julien Baste, Dimitrios M. Thilikos

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Julien Baste
Dimitrios M. Thilikos

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Julien Baste and Dimitrios M. Thilikos. Contraction-Bidimensionality of Geometric Intersection Graphs. In 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 89, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.IPEC.2017.5

Abstract

Given a graph G, we define bcg(G) as the minimum k for which G can be contracted to the uniformly triangulated grid Gamma_k. A graph class G has the SQGC property if every graph G in G has treewidth O(bcg(G)c) for some 1 <= c < 2. The SQGC property is important for algorithm design as it defines the applicability horizon of a series of meta-algorithmic results, in the framework of bidimensionality theory, related to fast parameterized algorithms, kernelization, and approximation schemes. These results apply to a wide family of problems, namely problems that are contraction-bidimensional. Our main combinatorial result reveals a general family of graph classes that satisfy the SQGC property and includes bounded-degree string graphs. This considerably extends the applicability of bidimensionality theory for several intersection graph classes of 2-dimensional geometrical objects.
Keywords
  • Grid exlusion theorem
  • Bidimensionality
  • Geometric intersection graphs
  • String Graphs

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