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- Mark de Berg, Amirali Khosravi
- COCOON
- 2010

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)

- Mark de Berg, Amirali Khosravi
- Int. J. Comput. Geometry Appl.
- 2012

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)

- Amirali Khosravi, Alireza Zarei, Mohammad Ghodsi
- CCCG
- 2007

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 complexification of real Hilbert C *-modules over real C *-algebras. We give an example of a Hilbert A c-module that is not the complexification of any Hilbert A-module, where A is a real C *-algebra.

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.

- Mohammad Ali Abam, Boris Aronov, Mark de Berg, Amirali Khosravi
- Symposium on Computational Geometry
- 2011

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)

- Mohammad Ali Abam, Mark de Berg, Amirali Khosravi
- WADS
- 2011

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.

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