Daniela Maftuleac

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We present and analyze methods for patrolling and surveillance in an environment with a distributed swarm of robots with limited capabilities. Our approach is based on a distributed triangulation of the work space, in which a set of p stationary sensors provides coverage control; in addition, there are r mobile robots that can move between the sensors.(More)
We present methods for patrolling and surveillance in an environment with a distributed swarm of robots with limited capabilities. We make use of a distributed triangulation of the work space, in which a set of n stationary sensors provides coverage control; in addition, there are k mobile robots that can move between the sensors. Building on our prior work(More)
CAT(0) metric spaces constitute a far-reaching common generalization of Euclidean and hyperbolic spaces and simple polygons: any two points x and y of a CAT(0) metric space are connected by a unique shortest path γ(x, y). In this paper, we present an efficient algorithm for answering two-point distance queries in CAT(0) rectangular complexes and two of(More)
CAT(0) metric spaces and hyperbolic spaces play an important role in combinatorial and geometric group theory. In this paper, we present efficient algorithms for distance problems in CAT(0) planar complexes. First of all, we present an algorithm for answering single-point distance queries in a CAT(0) planar complex. Namely, we show that for a CAT(0) planar(More)
We investigate the problem of determining if a given graph corresponds to the dual of a triangulation of a simple polygon. This is a graph recognition problem, where in our particular case we wish to recognize a graph which corresponds to the dual of a triangulation of a simple polygon with or without holes and interior points. We show that the difficulty(More)
We give lower bounds for various natural nodeand edgebased local strategies for exploring a graph. We consider this problem both in the setting of an arbitrary graph as well as the abstraction of a geometric exploration of a space by a robot, both of which have been extensively studied. We consider local exploration policies that use time-oflast-visit or(More)
Globally non-positively curved, or CAT(0), polyhedral complexes arise in a number of applications, including evolutionary biology and robotics. These spaces have unique shortest paths and are composed of Euclidean polyhedra, yet many properties of convex hulls in Euclidean space fail to transfer over. We give examples of some such properties. For(More)