Boaz Ben-Moshe

Joint cluster analysis of attribute data and relationship data: The connected k -center problem, algorithms and applications

Attribute data and relationship data are two principal types of data, representing the intrinsic and extrinsic properties of entities. While attribute data have 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 carry complementary information such as in market segmentation and community identification, which calls for a joint cluster analysis of both data types so as to achieve better results. In this article, we introduce the novel Connected k-Center (CkC) problem, a clustering model taking into account attribute data as well as relationship data. We analyze the complexity of the problem and prove its NP-hardness. Therefore, we analyze the approximability of the problem and also present a constant factor approximation algorithm. For the special case of the CkC problem where the relationship data form a tree structure, we propose a dynamic programming method giving an optimal solution in polynomial time. We further present NetScan, a heuristic algorithm that is efficient and effective for large real databases. Our extensive experimental evaluation on real datasets demonstrates the meaningfulness and accuracy of the NetScan results.

A Constant-Factor Approximation Algorithm for Optimal 1.5D Terrain Guarding

We present the first constant-factor approximation algorithm for a nontrivial instance of the optimal guarding (coverage) problem in polygons. In particular, we give an

Visibility preserving terrain simplification: an experimental study

O(1)

Efficient algorithms for center problems in cactus networks

-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 approximations follow from set cover results, our new results exploit the geometric structure of terrains to obtain a substantially improved approximation algorithm.

OBNOXIOUS FACILITY LOCATION: COMPLETE SERVICE WITH MINIMAL HARM

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 error is measured with respect to distance (e.g., Hausdorff) from the original or with respect to visual similarity. In this paper, we propose a new method of simplifying terrain surfaces, designed specifically to maximize a new measure of quality based on preserving inter-point visibility relationships. Our work is motivated by various problems of terrain analysis that rely on inter-point visibility relationships, such as optimal antenna placement.We have implemented our new method and give experimental evidence of its effectiveness in simplifying terrains according to our quality measure. We experimentally compare its performance with that of other leading simplification methods.

Efficient algorithms for the weighted 2-center problem in a cactus graph

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(nlogn) time algorithm to solve the 1-center problem, and an O(nlog^3n) time algorithm to solve the weighted continuous 2-center problem. We have also provided improved solutions to the general p-center problems in cactus networks. The developed ideas are then applied to solve the obnoxious 1-center problem in weighted cactus networks.

Approximating the Visible Region of a Point on a Terrain

We present efficient algorithms for several instances of the following facility location problem. Place k obnoxious facilities, with respect to n given demand sites and m given regions, where the goal is to maximize the minimal distance between a demand site and a facility, under the constraint that each of the regions must contain at least one facility. We also present an efficient solution to the following planar problem that arises as a subproblem. Given n transmitters, each of range r, construct a compact data structure that supports coverage queries, i.e., determine whether a query polygonal/rectangular region is fully covered by the transmitters.

Automated antenna positioning algorithms for wireless fixed-access networks

In this paper, we provide efficient algorithms for solving the weighted center problems in a cactus graph. In particular, an O(n logn) 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 log3n) time algorithm is devised for its continuous version and showed that its discrete version is solvable in O(n log2n) time. No such algorithm was previously known. The obnoxious center problem in a cactus graph can now be solved in O(n log3n). This improves the previous result of O(cn) where c is the number of distinct vertex weights used in the graph [8]. In the worst case c is O(n).

An optimal algorithm for the continuous/discrete weighted 2-center problem in trees

Given a terrain 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 interpolates the visible region between two consecutive rays (emanating from p) whenever the rays are close enough; that is, whenever the difference between the sets of visible segments along the cross sections in the directions specified by the rays is below some threshold. Thus the density of the sampling by rays is sensitive to the shape of the visible region. We suggest a specific way to measure the resemblance (difference) and to interpolate the visible region between two consecutive rays. We also present an alternative algorithm, which uses circles of increasing radii centered at p instead of rays emanating from p. Both algorithms compute a representation of the (approximated) visible region that is especially suitable for is-visible-from-p queries, i.e., given a query point q on the terrain determine whether q is visible from p. Finally, we report on the experiments that we performed with these algorithms and with their corresponding fixed versions, using a natural error measure. Our main conclusion is that the radar-like algorithm is significantly better than the others.

A real-time motion planning algorithm for a hyper-redundant set of mechanisms

Abstract This article addresses a real-life problem - obtaining communication links between multiple base station sites, by positioning a minimal set of fixed-access relay antenna sites on a given terrain. Reducing the number of relay antenna sites is considered critical due to substantial installation and maintenance costs. Despite the significant cost saved by eliminating even a single antenna site, an inefficient manual approach is employed due to the computational complexity of the problem. From the theoretical point of view we show that this problem is not only NP hard, but also does not have a constant approximation. In this paper we suggest several alternative automated heuristics, relying on terrain preprocessing to find educated potential points for positioning relay stations. A large-scale computer-based experiment consisting of approximately 7,000 different scenarios was conducted. The quality of alternative solutions was compared by isolating and displaying factors that were found to affect the standard deviation of the solutions supplied by the tested heuristics. The results of the simulation based experiments show that the saving potential increases when more base stations are needed to be interconnected. The designs of a human expert were compared to the automatically generated solutions for a small subset of the experiment scenarios. Our studies indicate that for small networks (e.g., connecting up to ten base stations), the results obtained by human experts are adequate although they rarely exceed the quality of automated alternatives. However, the process of obtaining these results in comparison to automated heuristics is longer. In addition, when more base station sites need to be interconnected, the human approach is easily outperformed by our heuristics, both in terms of better results (fewer antennas) and in significant shorter calculation times.