Computing Triangulations with Minimum Stabbing Number
نویسندگان
چکیده
For a given point set P or a polygon P , we consider the problem of finding a triangulation T with minimum stabbing number, i.e., a triangulation such that the maximal number of segments hit by any ray going through T is minimized. We prove that this problem is NP-hard; this differs from the problem of triangulating a polygon with minimum edge weight, which is solvable in polynomial time with a simple dynamic program [7]. In an experimental part we test various heuristics.
منابع مشابه
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The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or triangulations of minimum stabbing number for a given set of points. The complexity of these problems has been a long-standing open question; in fact, it is one of the or...
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Let P be a rectilinear simple polygon. The stabbing number of a partition of P into rectangles is the maximum number of rectangles stabbed by any axis-parallel segment inside P . We present a 3-approximation algorithm for finding a partition with minimum stabbing number. It is based on an algorithm that finds an optimal partition for histograms.
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Let S be a set of n points in R, and let r be a parameter with 1 6 r 6 n. A rectilinear r-partition for S is a collection Ψ(S) := {(S1, b1), . . . , (St, bt)}, such that the sets Si form a partition of S, each bi is the bounding box of Si, and n/2r 6 |Si| 6 2n/r for all 1 6 i 6 t. The (rectilinear) stabbing number of Ψ(S) is the maximum number of bounding boxes in Ψ(S) that are intersected by a...
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In this note, we report an error in our paper “Computing Partitions of Rectilinear Polygons with Minimum Stabbing Number” [2]. Given an orthogonal polygon P and a partition of P into rectangles, the stabbing number of the partition is defined as the maximum number of rectangles stabbed by any orthogonal line segment inside P . Abam et al. [1] introduced the problem of finding a partition of P i...
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