We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (t j) and radii (r j) that cover a given set of demand points Y ⊂ R 2 at the smallest possible cost. We consider cost functions of the form ∑ j f(r j), where f(r) = r α is the cost of transmission to radius r. Special cases arise for α = 1 (sum of radii) and α = 2 (total area); power consumption models in wireless network design often use an exponent α> 2. Different scenarios arise according to possible restrictions on the transmission centers t j, which may be constrained to belong to a given discrete set or to lie on a line, etc. We obtain several new results, including (a) exact and approximation algorithms for selecting transmission points t j on a given line in order to cover demand points Y ⊂ R 2; (b) approximation algorithms (and an algebraic intractability result) for selecting an optimal line on which to place transmission points to cover Y; (c) a proof of NP-hardness for a discrete set of transmission points in R 2 and any fixed α> 1; and (d) a polynomial-time approximation scheme for the problem of computing a minimum cost covering tour (MCCT), in which the total cost is a linear combination of the transmission cost for the set of disks and the length of a tour/path that connects the centers of the disks. ACM Classification: F.2.2 Nonnumerical Algorithms and Problems. AMS Classification: 68Q25, 68U05, 90C27.

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Abstract — Our objective is to automatically track and capture photos of an intruder using a robotic pan-tiltzoom camera. In this paper, we consider the problem of automated position estimation using a wireless network of inexpensive binary motion sensors. The challenge is to incorporate data from a network of noisy sensors that suffer from refractory periods during which they may be unresponsive. We propose an estimation method based on Particle Filtering, a numerical sequential Monte Carlo technique. We model sensors with conditional probability density functions and incorporate a probabilistic model of an intruder’s state that utilizes velocity. We present simulation and experiments with passive infrared (PIR) motion sensors that suggest that our estimator is effective and degrades gracefully with increasing sensor refractory periods.

This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wall-following motions and can traverse the interior of the environment only when following parallel to an edge. The robot has no global sensors that would allow precise mapping or localization. Special information spaces are introduced for this particular model. Using these, strategies are presented for solving several tasks: 1) counting vertices, 2) computing the path winding number, 3) learning a combinatorial map, called the cut ordering, that encodes partial geometric information, and 4) solving pursuit-evasion problems.