We show that every segment endpoint visibility graph on disjoint line segments in the plane admits an alternating path of length , answering a question of Bose. This bound is optimal apart from a constant factor. We also give bounds on the constants hidden by the asymptotic notation.

We show that the segment endpoint visibility graph of any finite set of 2n line segments contains a planar matching that does not use any segment edge, if the line segments in our set are convexly independent.

We consider visibility graphs involving bars and arcs in which lines of sight can pass through at most k objects. We prove a new edge bound for arc k-visibility graphs, provide maximal constructions for arc visibility graphs and semi-arc k-visibility graphs, and give a complete characterization of semi-arc visibility graphs. We further show that the family of arc i-visibility graphs is never co...

We define a natural class of graphs by generalizing prior notions of visibility, allowing the representing regions and sightlines to be arbitrary. We consider mainly the case of compact connected representing regions, proving two results giving necessary properties of visibility graphs, and giving some examples of classes of graphs that can be so represented. Finally, we give some applications ...

In this paper, we are concerned with computing and maintaining the exact visibility polygon V (q) of a moving point observer q in planar scenes represented by a polygon with holes with complexity of n. We propose an algorithm that applies and computes each change to V (q) in constant time as q moves to a new neighboring position. In fact, in our method changes to V (q), as the observer q moves,...

This paper surveys recent studies of learning problems in which the learner faces restrictions on the amount of information he can extract from each example he encounters. Our main framework for the analysis of such scenarios is the RFA (Restricted Focus of Attention) model. While being a natural reenement of the PAC learning model, some of the fundamental PAC-learning results and techniques fa...

A review of the archeological and non-archeological use of visibility networks reveals the use of a limited range of formal techniques, in particular for representing visibility theories. This paper aims to contribute to the study of complex visual relational phenomena in landscape archeology by proposing a range of visibility network patterns and methods. We propose firstand second-order visib...

Given a collection of polygonal obstacles with n vertices on the place, and any t > 1, we present an O(n logn) time algorithm that constructs a bounded-degree t-spanner of the visibility graph, without rst having to construct the visibility graph.

The visibility graph V(X) of a discrete point set X ⊂ R has vertex set X and an edge xy for every two points x, y ∈ X whenever there is no other point in X on the line segment between x and y. We show that for every graphG, there is a point setX ∈ R, such that the subgraph of V(X∪Z) induced by X is isomorphic to G. As a consequence, we show that there are visibility graphs of arbitrary high chr...