Following the seminal works of Danzer (1956, 1986) and Stach\'{o} ( 1965, 1981) , and the recent result of Har-Peled et. al. (2018), we study the problem of stabbing disks by points. We prove that any set of pairwise intersecting disks in the plane can be stabbed by four points. Our proof\etal  is constructive and yields a linear-time algorithm for finding the points .
In their seminal work, Danzer (1956, 1986) and Stach\'{o} ( 1981) established that every set of pairwise intersecting disks in the plane can be stabbed by four points. However, both these proofs are non-constructive, at least in the sense that they do not seem to imply an efficient algorithm for finding the stabbing points, given such a set of disks D. Recently, Har-Peled\etal (2018) presented a relatively simple linear-time algorithm for finding five points that stab D. We present an alternative proof (and the first in English) to the assertion that four points are sufficient to stab D. Moreover, our proof is constructive and provides a simple linear-time algorithm for finding the stabbing points. As a warmup, we present a nearly-trivial liner-time algorithm with an elementary proof for finding five points that stab D .
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Following the seminal works of
In their seminal work,
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1965,
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, and the recent result of Har-Peled et. al. (2018), we study the problem of stabbing disks by points. We prove that any
established that every
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Our proof
However, both these proofs are non-constructive, at least in the sense that they do not seem to imply an efficient algorithm for finding the stabbing points, given such a set of disks D. Recently, Har-Peled
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(2018) presented a relatively simple linear-time algorithm for finding five points that stab D. We present an alternative proof (and the first in English) to the assertion that four points are sufficient to stab D. Moreover, our proof
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yields a
provides a simple
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points
stabbing points. As a warmup, we present a nearly-trivial liner-time algorithm with an elementary proof for finding five points that stab D