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12
Minimumcost coverage of point sets by disks
 in Symposium on Computational Geometry
, 2006
"... 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) = ..."
Abstract

Cited by 15 (2 self)
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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 NPhardness for a discrete set of transmission points in R 2 and any fixed α> 1; and (d) a polynomialtime 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.
Online searching with turn cost
, 2004
"... We consider the problem of searching for an object on a line at an unknown distance OPT from the original position of the searcher, in the presence of a cost of d for each time the searcher changes direction. This is a generalization of the wellstudied linearsearch problem. We describe a strategy ..."
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Cited by 8 (2 self)
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We consider the problem of searching for an object on a line at an unknown distance OPT from the original position of the searcher, in the presence of a cost of d for each time the searcher changes direction. This is a generalization of the wellstudied linearsearch problem. We describe a strategy that is guaranteed to find the object at a cost of at most 9 · OPT + 2d, which has the optimal competitive ratio 9 with respect to OPT plus the minimum corresponding additive term. Our argument for upper and lower bound uses an infinite linear program, which we solve by experimental solution of an infinite series of approximating finite linear programs, estimating the limits, and solving the resulting recurrences for an explicit proof of optimality. We feel that this technique is interesting in its own right and should help solve other searching problems. In particular, we consider the star search or cowpath problem with turn cost, where the hidden object is placed on one of m rays emanating from the original position of the searcher. For this problem we give a tight bound of 1 + 2 m m (m−1) m−1 OPT+m
Automated intruder tracking using particle filtering and a network of binary motion sensors
 in IEEE International Conference on Automation Science and Engineering (CASE’06
, 2006
"... Abstract — Our objective is to automatically track and capture photos of an intruder using a robotic pantiltzoom 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 ..."
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Cited by 5 (3 self)
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Abstract — Our objective is to automatically track and capture photos of an intruder using a robotic pantiltzoom 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.
Mapping and PursuitEvasion Strategies For a Simple WallFollowing Robot
"... This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wallfollowing 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 pr ..."
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Cited by 1 (1 self)
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This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wallfollowing 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 pursuitevasion problems.
Searching and Mapping among Indistinguishable Convex Obstacles
"... Abstract — We present exploration and mapping strategies for a mobile robot moving among a finite collection of convex obstacles in the plane. The obstacles are unknown to the robot, which does not have access to coordinates and cannot measure distances or angles. The robot has a unique sensor, call ..."
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Abstract — We present exploration and mapping strategies for a mobile robot moving among a finite collection of convex obstacles in the plane. The obstacles are unknown to the robot, which does not have access to coordinates and cannot measure distances or angles. The robot has a unique sensor, called the gap sensor, that tracks the direction of the depth discontinuities in the robot’s visibility region. Furthermore, the robot can only move towards depth discontinuities. As the robot moves, the depth discontinuities split and merge, and these changes are encoded in a Gap Navigation Tree. We present a strategy for this robot that is guaranteed to explore the whole environment, but that cannot decide whether the exploration has been completed. If in addition it is assumed that the robot has access to a pebble, which is an identifiable point that the robot can manipulate, then we prove that the robot can decide (in polynomial time in the number of obstacles) whether the environment has been completely explored. For this, the robot is able to distinguish every obstacle using only the gap sensor and a single pebble. These results are a continuation of our previous work on gap sensing for multiply connected environments [24], in which we reduce the sensing requirements for the robot by constraining the shape of the obstacles. I.
1 Mapping and PursuitEvasion Strategies For a Simple WallFollowing Robot
"... Abstract—This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wallfollowing motions and can traverse the interior of the environment only when following parallel to an edge. The robot has no global sensors that would ..."
Abstract
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Abstract—This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wallfollowing 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 pursuitevasion problems. I.
1 Mapping and PursuitEvasion Strategies For a Simple WallFollowing Robot
"... Abstract—This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wallfollowing motions and can traverse the interior of the environment only when following parallel to an edge. The robot has no global sensors that would ..."
Abstract
 Add to MetaCart
Abstract—This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wallfollowing 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 pursuitevasion problems. Index Terms—Exploration, information spaces, minimal sensing, pursuitevasion, SLAM. I.
MinimumCost Coverage of Point Sets by Disks ∗ Helmut Alt
"... 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) = ..."
Abstract
 Add to MetaCart
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 strategies for maintaining a chain of relays between an explorer and a base camp
 THEORETICAL COMPUTER SCIENCE
, 2009
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