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Conference Papers Year : 2018

Contraction-Bidimensionality of Geometric Intersection Graphs

Abstract

Given a graph G, we define bcg(G) as the minimum k for which G can be contracted to the uniformly triangulated grid Γ k. A graph class G has the SQGC property if every graph G ∈ 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.
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lirmm-01890527 , version 1 (08-10-2018)

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Julien Baste, Dimitrios M. Thilikos. Contraction-Bidimensionality of Geometric Intersection Graphs. IPEC 2017 - 12th International Symposium on Parameterized and Exact Computation, Sep 2017, Vienne, Austria. pp.5:1--5:13, ⟨10.4230/LIPIcs.IPEC.2017.5⟩. ⟨lirmm-01890527⟩
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