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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)

We study the problem of computing the visibility graph defined by a set <i>P</i> of <i>n</i> points inside a polygon <i>Q</i>: two points <i>p</i>,<i>q</i> ε <i>P</i> are joined by an edge if the segment ‾<i><sub>pq</sub></i> ⊂ <i>Q</i>. Efficient output-sensitive algorithms are known for the case in which <i>P</i> is the set of all… (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 R p that is visible from p. We present a generic radar-like algorithm for computing an approximation of R p. 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… (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 3 n) time algorithm is devised for its continuous… (More)

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… (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 1-center problem, an O(n log 3 n) time algorithm to solve the weighted continuous 2-center problem. We have also… (More)