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- W2963303948 abstract "We study a class of geometric covering and packing problems for bounded closed regions on the plane. We are given a set of axis-parallel line segments that induce a planar subdivision with bounded (rectilinear) faces. We are interested in the following problems. (P1) Stabbing-Subdivision:Stab all closed bounded faces by selecting a minimum number of points in the plane.(P2) Independent-Subdivision:Select a maximum size collection of pairwise non-intersecting closed bounded faces.(P3) Dominating-Subdivision:Select a minimum size collection of bounded faces such that every other face has a non-empty intersection (i.e., sharing an edge or a vertex) with some selected face.We show that these problems are (mathsf { NP })-hard. We even prove that these problems are (mathsf { NP })-hard when we concentrate only on the rectangular faces of the subdivision. Further, we provide constant factor approximation algorithms for the Stabbing-Subdivision problem." @default.
- W2963303948 created "2019-07-30" @default.
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- W2963303948 date "2018-12-21" @default.
- W2963303948 modified "2023-09-23" @default.
- W2963303948 title "Covering and Packing of Rectilinear Subdivision" @default.
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- W2963303948 doi "https://doi.org/10.1007/978-3-030-10564-8_30" @default.
- W2963303948 hasPublicationYear "2018" @default.
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