Connecting a Set of Circles with Minimum Sum of Radii

Abstract. We consider the problem of assigning radii to a given set of points in the plane, such that the resulting set of circles is connected, and the sum of radii is minimized. We show that the problem is polynomially solvable if a connectivity tree is given. If the connectivity tree is unknown, the problem is NP-hard if there are upper bounds on the radii and open otherwise. We give approximation guarantees for a variety of polynomialtime algorithms, describe upper and lower bounds (which are matching in some of the cases), provide polynomial-time approximation schemes, and conclude with experimental results and open problems

Cooperative area surveillance strategies using multiple unmanned systems

Recently, the U.S. Department of Defense placed the technological development of intelligence, surveillance, and reconnaissance (ISR) tools at the top of its priority list. Area surveillance that takes place in an urban setting is an ISR tool of special interest. Unmanned aerial vehicles (UAVs) are ideal candidates to perform area surveillance because they are inexpensive and they do not require a human pilot to be aboard. Multiple unmanned systems increase the rate of information flow from the target region and maintain up to date information. The purpose of the research described in this dissertation is to develop and test a system that coordinates multiple UAVs on a wide area coverage surveillance mission. The research presented in this document implements a waypoint generator for multiple aerial vehicles that is especially suited for large area surveillance. The system chooses initial locations for the vehicles and generates a set of balanced sub-trees which cover the region of interest (ROI) for the vehicles. The sub-trees are then optimally combined to form a single minimal tree that spans the entire region. The system transforms the tree path into a series of waypoints suitable for the aerial vehicles. The output of the system is a set of waypoints for each vehicle assigned to the coverage task. Results from computer simulation and flight testing are presented.Ph.D.Committee Chair: Dr. George Vachtsevanos; Committee Member: Ayanna Howard; Committee Member: Dr. Thomas Michaels; Committee Member: Eric Johnson; Committee Member: Linda Will

The minimum area spanning tree problem

Abstract. Motivated by optimization problems in sensor coverage, we formulate and study the Minimum-Area Spanning Tree (mast) problem: Given a set P of n points in the plane, find a spanning tree of P of minimum “area, ” where the area of a spanning tree T is the area of the union of the n − 1 disks whose diameters are the edges in T. We prove that the Euclidean minimum spanning tree of P is a constant-factor approximation for mast. We then apply this result to obtain constant-factor approximations for the Minimum-Area Range Assignment (mara) problem, for the Minimum-Area Connected Disk Graph (macdg) problem, and for the Minimum-Area Tour (mat) problem. The first problem is a variant of the power assignment problem in radio networks, the second problem is a related natural problem, and the third problem is a variant of the traveling salesman problem.