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- Mohammad Ali Abam, Mark de Berg
- Symposium on Computational Geometry
- 2005

Let S be a set of n points moving on the real line. The kinetic sorting problem is to maintain a data structure on the set S that makes it possible to quickly generate a sorted list of the points inâ€¦ (More)

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

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 line segment inside P. We present aâ€¦ (More)

- Mohammad Ali Abam, Mark de Berg, Mohammad Farshi, Joachim Gudmundsson
- Discrete & Computational Geometry
- 2007

We introduce the concept of region-fault tolerant spanners for planar point sets, and prove the existence of region-fault tolerant spanners of small size. For a geometric graph <i>G</i> on a pointâ€¦ (More)

- Mohammad Ali Abam, Sariel Har-Peled
- Symposium on Computational Geometry
- 2010

We present a new optimal construction of semi-separated pair decomposition (SSPD) for a set of <i>n</i> points in IR<sup><i>d</i></sup>. In the new construction each point participates in a fewâ€¦ (More)

- Mohammad Ali Abam, Mark de Berg, Peter Hachenberger, Alireza Zarei
- Symposium on Computational Geometry
- 2007

We study the following variant of the well-known line-simpli-ficationproblem: we are getting a possibly infinite sequence of points p0,p1,p2,... in the plane defining a polygonal path, and asâ€¦ (More)

A Semi-Separated Pair Decomposition (SSPD), with parameter s > 1, of a set S âŠ‚ R is a set {(Ai, Bi)} of pairs of subsets of S such that for each i, there are balls DAi and DBi containing Ai and Biâ€¦ (More)

- Mohammad Ali Abam, Mark de Berg, Joachim Gudmundsson
- Symposium on Computational Geometry
- 2008

We present a new and simple (1+Îµ)-spanner of size <i>O</i>(<i>n</i>Îµ<sup>2</sup>) for a set of <i>n</i> points in the plane, which can be maintained efficiently as the points move. Assuming theâ€¦ (More)

Background. Consider a cellular network consisting of a set of base stations, where the signal from a given base station can be received by clients within a certain distance from the base station. Inâ€¦ (More)

- Mohammad Ali Abam, Marjan Adeli, Hamid Homapour, Pooya Zafar Asadollahpoor
- Symposium on Computational Geometry
- 2015

Let P be a set of n points inside a polygonal domain D. A polygonal domain with h holes (or obstacles) consists of h disjoint polygonal obstacles surrounded by a simple polygon which itself acts asâ€¦ (More)

Let S be a set S of n points on a polyhedral terrain T in R, and let Îµ > 0 be a fixed constant. We prove that S admits a (2 + Îµ)-spanner with O(n log n) edges with respect to the geodesic distance.â€¦ (More)