Planar support for non-piercing regions and applications

Rajiv Raman, Saurabh Ray

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given a hypergraph H = (X, S), a planar support for H is a planar graph G with vertex set X, such that for each hyperedge S ∈ S, the sub-graph of G induced by the vertices in S is connected. Planar supports for hypergraphs have found several algorithmic applications, including several packing and covering problems, hypergraph coloring, and in hypergraph visualization. The main result proved in this paper is the following: given two families of regions R and B in the plane, each of which consists of connected, non-piercing regions, the intersection hypergraph HR(B) = (B,{Br}r∈R), where Br = {b ∈ B: b ∩ r ≠ θ} has a planar support. Further, such a planar support can be computed in time polynomial in |R|, |B|, and the number of vertices in the arrangement of the regions in R ∪ B. Special cases of this result include the setting where either the family R, or the family B is a set of points. Our result unifies and generalizes several previous results on planar supports, PTASs for packing and covering problems on non-piercing regions in the plane and coloring of intersection hypergraph of non-piercing regions.

Original languageEnglish (US)
Title of host publication26th European Symposium on Algorithms, ESA 2018
EditorsHannah Bast, Grzegorz Herman, Yossi Azar
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Volume112
ISBN (Print)9783959770811
DOIs
StatePublished - Aug 1 2018
Event26th European Symposium on Algorithms, ESA 2018 - Helsinki, Finland
Duration: Aug 20 2018Aug 22 2018

Other

Other26th European Symposium on Algorithms, ESA 2018
CountryFinland
CityHelsinki
Period8/20/188/22/18

Fingerprint

Coloring
Visualization
Polynomials

Keywords

  • Geometric optimization
  • Non-piercing regions
  • Packing and covering

ASJC Scopus subject areas

  • Software

Cite this

Raman, R., & Ray, S. (2018). Planar support for non-piercing regions and applications. In H. Bast, G. Herman, & Y. Azar (Eds.), 26th European Symposium on Algorithms, ESA 2018 (Vol. 112). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ESA.2018.69

Planar support for non-piercing regions and applications. / Raman, Rajiv; Ray, Saurabh.

26th European Symposium on Algorithms, ESA 2018. ed. / Hannah Bast; Grzegorz Herman; Yossi Azar. Vol. 112 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Raman, R & Ray, S 2018, Planar support for non-piercing regions and applications. in H Bast, G Herman & Y Azar (eds), 26th European Symposium on Algorithms, ESA 2018. vol. 112, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 26th European Symposium on Algorithms, ESA 2018, Helsinki, Finland, 8/20/18. https://doi.org/10.4230/LIPIcs.ESA.2018.69
Raman R, Ray S. Planar support for non-piercing regions and applications. In Bast H, Herman G, Azar Y, editors, 26th European Symposium on Algorithms, ESA 2018. Vol. 112. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018 https://doi.org/10.4230/LIPIcs.ESA.2018.69
Raman, Rajiv ; Ray, Saurabh. / Planar support for non-piercing regions and applications. 26th European Symposium on Algorithms, ESA 2018. editor / Hannah Bast ; Grzegorz Herman ; Yossi Azar. Vol. 112 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018.
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