Holes in 2-convex point sets

Oswin Aichholzer, Martin Balko, Thomas Hackl, Alexander Pilz, Pedro Ramos, Pavel Valtr, Birgit Vogtenhuber

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

Abstract

Let S be a set of n points in the plane in general position (no three points from S are collinear). For a positive integer k, a k-hole in S is a convex polygon with k vertices from S and no points of S in its interior. For a positive integer l, a simple polygon P is l-convex if no straight line intersects the interior of P in more than l connected components. A point set S is l-convex if there exists an l-convex polygonization of S. Considering a typical Erdős-Szekeres-type problem, we show that every 2-convex point set of size n contains an Ω(log n)-hole. In comparison, it is well known that there exist arbitrarily large point sets in general position with no 7-hole. Further, we show that our bound is tight by constructing 2-convex point sets with holes of size at most O(log n).

Originalspracheenglisch
TitelCombinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers
Herausgeber (Verlag)Springer Verlag Heidelberg
Seiten169-181
Seitenumfang13
Band10765
ISBN (Print)9783319788241
DOIs
PublikationsstatusVeröffentlicht - 1 Jan 2018
Veranstaltung28th International Workshop on Combinational Algorithms, IWOCA 2017 - Newcastle, NSW, Australien
Dauer: 17 Jul 201721 Jul 2017

Publikationsreihe

NameLecture Notes in Computer Science
Band10765
ISSN (Print)0302-9743
ISSN (elektronisch)1611-3349

Konferenz

Konferenz28th International Workshop on Combinational Algorithms, IWOCA 2017
LandAustralien
OrtNewcastle, NSW
Zeitraum17/07/1721/07/17

Schlagwörter

    ASJC Scopus subject areas

    • !!Theoretical Computer Science
    • !!Computer Science(all)

    Fingerprint Untersuchen Sie die Forschungsthemen von „Holes in 2-convex point sets“. Zusammen bilden sie einen einzigartigen Fingerprint.

  • Dieses zitieren

    Aichholzer, O., Balko, M., Hackl, T., Pilz, A., Ramos, P., Valtr, P., & Vogtenhuber, B. (2018). Holes in 2-convex point sets. in Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers (Band 10765, S. 169-181). (Lecture Notes in Computer Science ; Band 10765 ). Springer Verlag Heidelberg. https://doi.org/10.1007/978-3-319-78825-8_14