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- W3022023143 abstract "Let $S$ and $D$ each be a set of orthogonal line segments in the plane. A line segment $sin S$ emph{stabs} a line segment $s'in D$ if $scap s'neqemptyset$. It is known that the problem of stabbing the line segments in $D$ with the minimum number of line segments of $S$ is NP-hard. However, no better than $O(log |Scup D|)$-approximation is known for the problem. In this paper, we introduce a constrained version of this problem in which every horizontal line segment of $Scup D$ intersects a common vertical line. We study several versions of the problem, depending on which line segments are used for stabbing and which line segments must be stabbed. We obtain several NP-hardness and constant approximation results for these versions. Our finding implies, the problem remains NP-hard even under the extra assumption on input, but small constant approximation algorithms can be designed." @default.
- W3022023143 created "2020-05-13" @default.
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- W3022023143 date "2019-01-01" @default.
- W3022023143 modified "2023-09-26" @default.
- W3022023143 title "Constrained Orthogonal Segment Stabbing." @default.
- W3022023143 hasPublicationYear "2019" @default.
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