TY - JOUR

T1 - Stabbing pairwise intersecting disks by five points

AU - Har-Peled, Sariel

AU - Kaplan, Haim

AU - Mulzer, Wolfgang

AU - Roditty, Liam

AU - Seiferth, Paul

AU - Sharir, Micha

AU - Willert, Max

N1 - Publisher Copyright:
© 2021 Elsevier B.V.

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

KW - Disk intersection graph

KW - LP-type problem

KW - Stabbing set

UR - http://www.scopus.com/inward/record.url?scp=85104361095&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2021.112403

DO - 10.1016/j.disc.2021.112403

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AN - SCOPUS:85104361095

SN - 0012-365X

VL - 344

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 7

M1 - 112403

ER -