Abstract
In this thesis, we study the problem of piercing pairwise intersecting disks in the plane. A set D of disks is said to be pierced by a point set P if each disk in D contains a point of P. Any set of pairwise intersecting unit disks can be pierced by 3 points, and any set of pairwise intersecting disks of arbitrary radius can be pierced by 4 points. However, existing algorithms for computing the piercing points all use the LP-type problem as a subroutine. We present a simple linear-time algorithm for finding 3 piercing points for pairwise intersecting unit disks and a simple linear-time algorithm for finding 5 piercing points for pairwise intersecting disks of arbitrary radius. Our algorithms use simple geometric transformation and avoid LP-type machinery. In this thesis, we also present a set of 9 pairwise intersecting unit disks that cannot be pierced by 2 points.
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