Stabbing pairwise intersecting disks by five points

Sariel Har-Peled, Haim Kaplan, Wolfgang Mulzer*, Liam Roditty, Paul Seiferth, Micha Sharir, Max Willert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Suppose we are given a set D of n pairwise intersecting disks in the plane. A planar point set P stabs D if and only if each disk in D contains at least one point from P. We present a deterministic algorithm that takes O(n) time to find five points that stab D. Furthermore, we give a simple example of 13 pairwise intersecting disks that cannot be stabbed by three points. Moreover, we present a simple argument showing that eight disks can be stabbed by at most three points. This provides a simple – albeit slightly weaker – algorithmic version of a classical result by Danzer that such a set D can always be stabbed by four points.

Original languageEnglish
Article number112403
JournalDiscrete Mathematics
Volume344
Issue number7
DOIs
StatePublished - Jul 2021

Funding

FundersFunder number
German–Israeli Science Foundation
Blavatnik Research Fund in Computer Science
European Research Council
ISF, Israel892/13, 260/18
ISAAC50:1–50:12
National Science FoundationCCF-1421231, CCF-1217462
Tel Aviv University1595-19
Horizon 2020 Framework Programme757609
Deutsche ForschungsgemeinschaftERCSTG 757609, MU/3501/1
Israeli Centers for Research Excellence4/11
Blavatnik Family Foundation1367/2016, 1161/2011

    Keywords

    • Disk intersection graph
    • LP-type problem
    • Stabbing set

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