Daniela Maftuleac

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CAT(0) metric spaces constitute a far-reaching common generalization of Euclidean and hyper-bolic 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)
— We present and analyze methods for patrolling an environment with a distributed swarm of robots. Our approach uses a physical data structure – a distributed triangulation of the workspace. A large number of stationary " mapping " robots cover and triangulate the environment and a smaller number of mobile " patrolling " robots move amongst them. The focus(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)
— Motivated by the modern availability of drones and unmanned surface vessels as well as other low cost search agents, we consider the problem of a swarm of robots searching for a target on the high seas. Coordinating such a search in an effective manner is a non trivial task. In this paper we fully address this problem by first developing an abstract model(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 node-and edge-based 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-of-last-visit or(More)
We consider the problem of multiple agents or robots searching for a target in the plane. This is motivated by Search and Rescue operations (SAR) in the high seas which in the past were often performed with several vessels, and more recently by swarms of aerial drones and/or unmanned surface vessels. Coordinating such a search in an effective manner is a(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)
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