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 -