Boaz Ben-Moshe

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We present the first constant-factor approximation algorithm for a non-trivial instance of the optimal guarding (coverage) problem in polygons. In particular, we give an <i>O</i>(1)-approximation algorithm for placing the fewest point guards on a 1.5D terrain, so that every point of the terrain is seen by at least one guard. While polylogarithmic-factor(More)
We present the first constant-factor approximation algorithm for a non-trivial instance of the optimal guarding (coverage) problem in polygons. In particular, we give an O(1)-approximation algorithm for placing the fewest point guards on a 1.5D terrain, so that every point of the terrain is seen by at least one guard. While polylogarithmic-factor(More)
Attribute data and relationship data are two principle types of data, representing the intrinsic and extrinsic properties of entities. While attribute data has been the main source of data for cluster analysis, relationship data such as social networks or metabolic networks are becoming increasingly available. It is also common to observe both data types(More)
The terrain surface simplification problem has been studied extensively, as it has important applications in geographic information systems and computer graphics. The goal is to obtain a new surface that is combinatorially as simple as possible, while maintaining a prescribed degree of similarity with the original input surface. Generally, the approximation(More)
Given a terrain T and a point p on or above it, we wish to compute the region Rp that is visible from p. We present a generic radar-like algorithm for computing an approximation of Rp. The algorithm extrapolates the visible region between two consecutive rays (emanating from p) whenever the rays are close enough; that is, whenever the difference between the(More)
Efficient algorithms for solving the center problems in weighted cactus networks are presented. In particular, we have proposed the following algorithms for the weighted cactus networks of size n: an O(n log n) time algorithm to solve the 1center problem, an O(n log 3n) time algorithm to solve the weighted continuous 2-center problem. We have also provided(More)
In this paper, we provide efficient algorithms for solving the weighted center problems in a cactus graph. In particular, an O(n log n) time algorithm is proposed that finds the weighted 1-center in a cactus graph, where n is the number of vertices in the graph. For the weighted 2-center problem, an O(n log n) time algorithm is devised for its continuous(More)
This thesis is in Computational Geometry. Computational Geometry is a subfield of Computer Science that deals with problems of a geometric nature that arise in application domains such as Computer Graphics, Robotics, Geographic Information Systems (GIS), and Molecular Biology. More specifically, in this thesis we conduct research in Computational Geometry(More)
We study several natural proximity and facility location problems that arise for a set ${\cal P}$ of $n$ points and a set $\R$ of $m$ disjoint rectangular obstacles in the plane, where distances are measured according to the $L_1$ shortest path (geodesic) metric. In particular, we compute, in time $O(mn\log(m+n))$, a data structure of size $O(mn)$ that(More)
In a classical facility location problem we consider a graph G with fixed weights on the edges of G. The goal is then to find an optimal positioning for a set of facilities on the graph with respect to some objective function. We introduce a new framework for facility location problems, where the weights on the graph edges are not fixed, but rather should(More)