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  1. No Access

    Article

    Preclustering Algorithms for Imprecise Points

    We study the problem of preclustering a set B of imprecise points in  \({\mathbb {R}}^d\) ...

    Mohammad Ali Abam, Mark de Berg, Sina Farahzad, Mir Omid Haji Mirsadeghi… in Algorithmica (2022)

  2. No Access

    Article

    Local Geometric Spanners

    We introduce the concept of local spanners for planar point sets with respect to a family of regions, and prove the existence of local spanners of small size for some families. For a geometric graph G on a point ...

    Mohammad Ali Abam, Mohammad Sadegh Borouny in Algorithmica (2021)

  3. No Access

    Book and Conference Proceedings

    Topics in Theoretical Computer Science

    Third IFIP WG 1.8 International Conference, TTCS 2020, Tehran, Iran, July 1–2, 2020, Proceedings

    Prof. Luís S. Barbosa… in Lecture Notes in Computer Science (2020)

  4. No Access

    Article

    Spanners for Geodesic Graphs and Visibility Graphs

    Let \(\mathcal{P}\) P ...

    Mohammad Ali Abam in Algorithmica (2018)

  5. No Access

    Chapter and Conference Paper

    Fault-Tolerant Spanners in Networks with Symmetric Directional Antennas

    Let P be a set of points in the plane, each equipped with a directional antenna that can cover a sector of angle \(\alpha \) ...

    Mohammad Ali Abam, Fatemeh Baharifard… in WALCOM: Algorithms and Computation (2017)

  6. No Access

    Chapter and Conference Paper

    Computing the Smallest Color-Spanning Axis-Parallel Square

    For a given set of n colored points with k colors in the plane, we study the problem of computing the smallest color-spanning axis-parallel square. First, for a dynamic set of colored points on the real line, we ...

    Payam Khanteimouri, Ali Mohades, Mohammad Ali Abam… in Algorithms and Computation (2013)

  7. No Access

    Chapter and Conference Paper

    Kinetic Pie Delaunay Graph and Its Applications

    We construct a new proximity graph, called the Pie Delaunay graph, on a set of n points which is a super graph of Yao graph and Euclidean minimum spanning tree (EMST). We efficiently maintain the Pi...

    Mohammad Ali Abam, Zahed Rahmati, Alireza Zarei in Algorithm Theory – SWAT 2012 (2012)

  8. Article

    Open Access

    Geometric Spanners for Weighted Point Sets

    Let (S,d) be a finite metric space, where each element p∈S has a non-negative weight w (p). We study spanners for the set S with respect to the following weighted distance function: $$\mathbf{...

    Mohammad Ali Abam, Mark de Berg, Mohammad Farshi, Joachim Gudmundsson… in Algorithmica (2011)

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  9. No Access

    Article

    Out-of-Order Event Processing in Kinetic Data Structures

    We study the problem of designing kinetic data structures (KDS’s for short) when event times cannot be computed exactly and events may be processed in a wrong order. In traditional KDS’s this can lead to major...

    Mohammad Ali Abam, Pankaj K. Agarwal, Mark de Berg, Hai Yu in Algorithmica (2011)

  10. Article

    Open Access

    Kinetic Spanners in ℝ d

    We present a new (1+ε)-spanner for sets of n points in ℝ d . Our spanner has size O(n/ε d−1) and maximum degree O(log  d ...

    Mohammad Ali Abam, Mark de Berg in Discrete & Computational Geometry (2011)

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  11. No Access

    Chapter and Conference Paper

    Piecewise-Linear Approximations of Uncertain Functions

    We study the problem of approximating a function F: ℝ → ℝ by a piecewise-linear function \(\overline{\mathrm{F}}\) when the values of F at ...

    Mohammad Ali Abam, Mark de Berg, Amirali Khosravi in Algorithms and Data Structures (2011)

  12. Article

    Open Access

    Kinetic Collision Detection for Convex Fat Objects

    We design compact and responsive kinetic data structures for detecting collisions between n convex fat objects in 3-dimensional space that can have arbitrary sizes. Our main results are:

      ...

    Mohammad Ali Abam, Mark de Berg, Sheung-Hung Poon, Bettina Speckmann in Algorithmica (2009)

    Download PDF (435 KB)

  13. No Access

    Chapter and Conference Paper

    Geometric Spanners for Weighted Point Sets

    Let (S,d) be a finite metric space, where each element p ∈ S has a non-negative weight w(p). We study spanners for the set S with respect to weighted distance function d w ...

    Mohammad Ali Abam, Mark de Berg, Mohammad Farshi… in Algorithms - ESA 2009 (2009)

  14. No Access

    Chapter and Conference Paper

    On the Power of the Semi-Separated Pair Decomposition

    A Semi-Separated Pair Decomposition (SSPD), with parameter s > 1, of a set \(S\subset {\mathbb R}^d\) is a set {(A ...

    Mohammad Ali Abam, Paz Carmi, Mohammad Farshi… in Algorithms and Data Structures (2009)

  15. No Access

    Chapter and Conference Paper

    Out-of-Order Event Processing in Kinetic Data Structures

    We study the problem of designing kinetic data structures (KDS’s for short) when event times cannot be computed exactly and events may be processed in a wrong order. In traditional KDS’s this can lead to major...

    Mohammad Ali Abam, Pankaj K. Agarwal, Mark de Berg, Hai Yu in Algorithms – ESA 2006 (2006)