In this paper we study the problem of gathering in the same location of the plane a collection of identical oblivious mobile robots. Previous investigations have focused mostly on the unlimited visibility setting, where each robot can always see all the other ones, regardless of their distance. In the more difficult and realistic setting where the robots have limited visibility, the existing al...

We address the problem of multi-robot area coverage and present a new approach in the case where the map of the area and its static obstacles are known and the robots have a limited visibility range. The proposed method starts by locating a set of static guards on the map of the target area and then builds a graph called Reduced-CDT, a new environment representation method based on the Constrai...

Orthogonal connectors are used in drawings of many types of network diagrams, especially those representing electrical circuits. One approach for routing such connectors has been to compute an orthogonal visibility graph formed by intersecting vertical and horizontal lines projected from the corners of all obstacles and then use an A* search over this graph. However the search can be slow since...

A shape visibility representation displays a graph so that each vertex is represented by an orthogonal polygon of a particular shape and for each edge there is a horizontal or vertical line of sight between the polygons assigned to its endvertices. Special shapes are rectangles, L, T, E and H-shapes, and caterpillars. A flat rectangle is a horizontal bar of height > 0. A graph is 1-planar if th...

Die selbständige und eigenhändige Anfertigung versichere ich an Eides statt. Conclusion 71 Bibliography 75 Introduction " The true mystery of the world is the visible, not the invisible. " Oscar Wilde How can geometric settings be encoded combinatorially? Which discrete structures extract the essential information from continuous arrangements? How can the combinatorial properties of visibility ...

In this research, we investigate the subject of path-finding. A pruned version of visibility graph based on Candidate Vertices is formulated, followed by a new visibility check technique. Such combination enables us to quickly identify the useful vertices and thus find the optimal path more efficiently. The algorithm proposed is demonstrated on various path-finding cases. The performance of the...

We investigate the role of the information available to the players on the outcome of the cops and robbers game. This game takes place on a graph and players move along the edges in turns. The cops win the game if they can move onto the robber’s vertex. In the standard formulation, it is assumed that the players can “see” each other at all times. A graph G is called cop-win if a single cop can ...

This paper considers representations of graphs as rectangle-visibility graphs and as doubly linear graphs. These are, respectively, graphs whose vertices are isothetic rectangles in the plane with adjacency determined by horizontal and vertical visibility, and graphs that can be drawn as the union of two straight-edged planar graphs. We prove that these graphs have, with n vertices, at most 6n−...

Given a set S of n non-intersecting line segments in the plane, we present an algorithm that computes the 2n visibility polygons of the endpoints of S, in output sensitive time. The algorithm relies on the ordered endpoint visibility graph information to traverse the endpoints of S in a spiral-like manner using a combination of Jarvis' March and depthrst search. One extension of this result is ...

An obstacle representation of a graph consists of a set of polygonal obstacles and a distinct point for each vertex such that two points see each other if and only if the corresponding vertices are adjacent. Obstacle representations are a recent generalization of classical polygon–vertex visibility graphs, for which the characterization and recognition problems are long-standing open questions....