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An optimal bsp for a set S of disjoint line segments in the plane is a bsp for S that produces the minimum number of cuts. We study optimal bsps for three classes of bsps, which differ in the splitting lines that can be used when partitioning a set of fragments in the recursive partitioning process: free bsps can use any splitting line, restricted bsps can… (More)

An optimal bsp for a set S of disjoint line segments in the plane is a bsp for S that produces the minimum number of cuts. We study optimal bsps for three classes of bsps, which differ in the splitting lines that can be used when partitioning a set of fragments in the recursive partitioning process: free bsps can use any splitting line, restricted bsps can… (More)

Let S be a set of n points in R d , and let r be a parameter with 1 r 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 |Si| 2n/r for all 1 i t. The (rectilinear) stabbing number of Ψ (S) is the maximum number of bounding boxes in Ψ… (More)

In this paper we consider maintaining the visibility of a segment observer moving inside a simple polygon. A practical instance of this problem is to identify the regions of a planar scene illuminated by a fluorescent lamp while the lamp moves around. We consider both strong and weak visibility in this paper. Our method is based on the shortest path tree… (More)

We study the problem of approximating a function F : R → R by a piecewise-linear function F when the values of F at {x1,. .. , xn} are given by a discrete probability distribution. Thus, for each xi we are given a discrete set yi,1,. .. , yi,m i of possible function values with associated probabilities pi,j such that Pr[F(xi) = yi,j] = pi,j.

Let <i>P</i> 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 line segment inside P. We present a 3-approximation algorithm for the problem of finding a partition with minimum stabbing number. It is based on an algorithm that finds an optimal partition… (More)

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