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- 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)

- 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)

- 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)

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… (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)

- 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,mi of possible function values with associated probabilities pi,j such that Pr[F(xi) = yi,j ] = pi,j . We define… (More)

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.

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

Suppose that a geometrically distributed number of observations are available from an absolutely continuous distribution function F , within this set of observations denote the random number of records by M . This is called geometric random record model. In this paper, characterizations of F are provided in terms of the subsequences entropies of records… (More)

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