Colorful strips

Greg Aloupis, Jean Cardinal, Sébastien Collette, Shinji Imahori, Matias Korman, Stefan Langerman, Oded Schwartz, Shakhar Smorodinsky, Perouz Taslakian

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

We study the following geometric hypergraph coloring problem: given a planar point set and an integer k, we wish to color the points with k colors so that any axis-aligned strip containing sufficiently many points contains all colors. We show that if the strip contains at least 2k-1 points, such a coloring can always be found. In dimension d, we show that the same holds provided the strip contains at least k(4ln k+ln d) points. We also consider the dual problem of coloring a given set of axis-aligned strips so that any sufficiently covered point in the plane is covered by k colors. We show that in dimension d the required coverage is at most d(k-1)+1. Lower bounds are also given for all of the above problems. This complements recent impossibility results on decomposition of strip coverings with arbitrary orientations. From the computational point of view, we show that deciding whether a three-dimensional point set can be 2-colored so that any strip containing at least three points contains both colors is NP-complete. This shows a big contrast with the planar case, for which this decision problem is easy.

本文言語English
ホスト出版物のタイトルLATIN 2010
ホスト出版物のサブタイトルTheoretical Informatics - 9th Latin American Symposium, Proceedings
ページ2-13
ページ数12
DOI
出版ステータスPublished - 2010 6月 18
イベント9th Latin American Theoretical Informatics Symposium, LATIN 2010 - Oaxaca, Mexico
継続期間: 2010 4月 192010 4月 23

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
6034 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other9th Latin American Theoretical Informatics Symposium, LATIN 2010
国/地域Mexico
CityOaxaca
Period10/4/1910/4/23

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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