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- W2016458081 abstract "We introduce the notion of the width bounded geometric separator and develop the techniques for the existence of the width bounded separator in any fixed d -dimensional Euclidean space. The separator is applied in obtaining 2 O ( n ) time exact algorithms for a class of NP-complete geometric problems, whose previous algorithms take n O ( n ) time. One of those problems is the well-known disk covering problem, which seeks to determine the minimal number of fixed size disks to cover n points on a plane. They also include some NP-hard problems on disk graphs such as the maximum independent set problem, the vertex cover problem, and the minimum dominating set problem. For a constant a > 0 and a set of points Q on the plane, an a -wide separator is the region between two parallel lines of distance a that partitions Q into Q 1 (on the left side of the region), S (inside the region), and Q 2 (on the right side of the region). If the distance is at least one between every two points in the set Q with n points, there is an a -wide separator that partitions Q into Q 1 , S and Q 2 such that | Q 1 | , | Q 2 | ⩽ ( 2 / 3 ) n , and | S | ⩽ 1.2126 a n . Our width bounded separator in d -dimensional Euclidean space with fixed d is controlled by two parallel hyper-planes, and is used to design 2 O ( n 1 − 1 d ) -time algorithms for the d -dimensional disk covering problem and the above other problems in the d -dimensional disk graphs." @default.
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- W2016458081 date "2011-03-01" @default.
- W2016458081 modified "2023-09-29" @default.
- W2016458081 title "Theory and application of width bounded geometric separators" @default.
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- W2016458081 doi "https://doi.org/10.1016/j.jcss.2010.05.003" @default.
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