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Sparse Outerstring Graphs Have Logarithmic Treewidth

Authors Shinwoo An, Eunjin Oh, Jie Xue

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Author Details

Shinwoo An
  • Pohang University of Science and Technology, South Korea
Eunjin Oh
  • Pohang University of Science and Technology, South Korea
Jie Xue
  • New York University Shanghai, China

Funding

The work by An and Oh was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2024-00358505).

Cite AsGet BibTex

Shinwoo An, Eunjin Oh, and Jie Xue. Sparse Outerstring Graphs Have Logarithmic Treewidth. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.10

Abstract

An outerstring graph is the intersection graph of curves lying inside a disk with one endpoint on the boundary of the disk. We show that an outerstring graph with n vertices has treewidth O(αlog n), where α denotes the arboricity of the graph, with an almost matching lower bound of Ω(α log (n/α)). As a corollary, we show that a t-biclique-free outerstring graph has treewidth O(t(log t)log n). This leads to polynomial-time algorithms for most of the central NP-complete problems such as Independent Set, Vertex Cover, Dominating Set, Feedback Vertex Set, Coloring for sparse outerstring graphs. Also, we can obtain subexponential-time (exact, parameterized, and approximation) algorithms for various NP-complete problems such as Vertex Cover, Feedback Vertex Set and Cycle Packing for (not necessarily sparse) outerstring graphs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Outerstring graphs
  • geometric intersection graphs
  • treewidth

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