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**public sources and our publisher partners.**The disjoint convex obstacle number of a graph G is the smallest number h such that there is a set of h pairwise disjoint convex polygons (obstacles) and a set of n points in the plane [corresponding… Continue Reading

The obstacle number of a graph G is the smallest number of polygonal obstacles in the plane with the property that the vertices of G can be represented by distinct points such that two of them see… Continue Reading

High-level structural information about macromolecules is now being organized into databases. One of the common ways of storing information in such databases is in the form of three-dimensional (3D)… Continue Reading

In this work, we apply geometric and combinatorial methods to explore a variety of problems motivated by wireless sensor networks. Imagine sensors capable of communicating along straight lines except… Continue Reading

Positioning disk-shaped sensors to optimize certain coverage parameters is a fundamental problem in ad hoc sensor networks. The hexagon lattice arrangement is known to be optimally efficient in the… Continue Reading

This chapter describes the progress of the Digital Government Research Center in tackling the challenges of integrating and accessing the massive amount of statistical and text data available from… Continue Reading

Motivated by questions in computer vision and sensor networks, Alpert et al. [3] introduced the following definitions. Given a graph G, an obstacle representation of G is a set of points in the plane… Continue Reading

An obstacle representation for a (straight-line) graph drawing consists of the positions of the graph vertices together with a set of polygonal obstacles such that every line segment between a pair… Continue Reading

An obstacle representation of a planar straight-line graph (PSLG) G consists of the choice and placement of a set of opaque polygonal obstacles in such a way that the visibility graph on V (G)… Continue Reading

An obstacle representation of a graph G is a set of points on the plane together with a set of polygonal obstacles that determine a visibility graph isomorphic to G. The obstacle number of G is the… Continue Reading