Ahmad Biniaz

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Given a set of n red points and n blue points in the plane, we are interested to match the red points with the blue points by straight line segments in such a way that the segments do not cross each other and the length of the longest segment is minimized. In general, this problem in NP-hard. We give exact solutions for some special cases of the input point(More)
Given a weighted graph G = (V,E) and a subset R of V , a Steiner tree in G is a tree which spans all vertices in R. The vertices in V \R are called Steiner vertices. A full Steiner tree is a Steiner tree in which each vertex of R is a leaf. The full Steiner tree problem is to find a full Steiner tree with minimum weight. The bottleneck full Steiner tree(More)
Let P be a set of n points in general position in the plane which is partitioned into color classes. P is said to be color-balanced if the number of points of each color is at most bn/2c. Given a color-balanced point set P , a balanced cut is a line which partitions P into two colorbalanced point sets, each of size at most 2n/3+1. A colored matching of P is(More)
This paper presents a new way to compute the Delaunay triangulation of a planar set P of n points, using sweep-circle technique combined with the standard recursive edge-flipping. The algorithm sweeps the plane by an increasing circle whose center is a fixed point in the convex hull of P . Empirical results and comparisons show that it reduces the number of(More)
We consider an extension of the triangular-distance Delaunay graphs (TD-Delaunay) on a set P of points in general position in the plane. In TD-Delaunay, the convex distance is defined by a fixed-oriented equilateral triangle 5, and there is an edge between two points in P if and only if there is an empty homothet of 5 having the two points on its boundary.(More)
Terrains are often modeled by triangulations and one of the criteria is that: triangulation should have “nice shape”. Delaunay triangulation is a good way to formalize nice shape. Another criterion is slope fidelity in terrains. In natural terrains there are no abrupt changes in slope. A triangulation for a terrain should use triangles of nice shape and(More)
Terrains are often modeled by triangulations. One of the criteria that a triangulation should have is “nice shape” triangles. Delaunay triangulation is a good way to formalize nice shape. Another criterion is reality of drainage in terrains. Natural terrains do not have many local minima and have drainage lines in the bottom of valleys. To achieve these(More)
Let R and B be two disjoint sets of points in the plane such that |B| 6 |R|, and no three points of R ∪ B are collinear. We show that the geometric complete bipartite graph K(R,B) contains a non-crossing spanning tree whose maximum degree is at most max { 3, ⌈ |R|−1 |B| ⌉ + 1 } ; this is the best possible upper bound on the maximum degree. This solves an(More)
A bottleneck plane perfect matching of a set of n points in R is defined to be a perfect non-crossing matching that minimizes the length of the longest edge; the length of this longest edge is known as bottleneck. The problem of computing a bottleneck plane perfect matching has been proved to be NP-hard. We present an algorithm that computes a bottleneck(More)
Let S be a finite set of points in the interior of a simple polygon P . A geodesic graph, GP (S,E), is a graph with vertex set S and edge set E such that each edge (a, b) ∈ E is the shortest geodesic path between a and b inside P . GP is said to be plane if the edges in E do not cross. If the points in S are colored, then GP is said to be properly colored(More)