The subject of multi-robot systems has been thoroughly investigated in the past decade (e.g., [9, 12, 11, 7]). Current research in multi-robot systems can be divided, roughly, according to two aspects: theoretical robotics (e.g. [12]) and practical robotics (e.g. [10]). Theoretical robotics research, in many cases, make unrealistic assumptions on the robots’ capabilities. For example, robots ar...

Rapidly Exploring Random Trees (RRT) and Probabilistic Roadmaps (PRM) are sampling based techniques being extensively used for robot path planning. In this paper the tree structure of the RRT is generalized to a graph structure which enables a greater exploration. Exploration takes place simultaneously from multiple points in the map, all explorations fusing at multiple points producing well-co...

hyperactivity disorder (ADHD) Ainara Mira-Iglesias; J. Alberto Conejero; Esperanza Navarro-Pardo Fundación para el Fomento de la Investigación Sanitaria y Biomédica de la Comunidad Valenciana (FISABIO), Valencia, Spain Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Spain Departamento de Psicoloǵıa Evolutiva y de la Educación, Universitat de València,...

A visibility representation of a graph G is an assignment of the vertices of G to geometric objects such that vertices are adjacent if and only if their corresponding objects are “visible” each other, that is, there is an uninterrupted channel, usually axis-aligned, between them. Depending on the objects and definition of visibility used, not all graphs are visibility graphs. In such situations...

Given an arbitrary polygon P with holes, we construct a polytopal complex analogous to the associahedron based on convex diagonalizations of P . This polytopal complex is shown to be contractible, and a geometric realization is provided based on the theory of secondary polytopes. We then reformulate a combinatorial deformation theory and present an open problem based on visibility which is a cl...

In this paper we give tight lower bounds on the size of the visibility graph, the contracted visibility graph, and the bar-visibility graph of n disjoint line segments in the plane, according to their vertex-connectivity.

We study polar visibility graphs, graphs whose vertices can be represented by arcs of concentric circles with adjacency determined by radial visibility including visibility through the origin. These graphs are more general than the well-studied bar-visibility graphs and are characterized here, when arcs are proper subsets of circles, as the graphs that embed on the plane with all but at most on...