Approximating Barrier Resilience in Wireless Sensor Networks
 Sergey Bereg,
 David Kirkpatrick
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Abstract
Barrier coverage in a sensor network has the goal of ensuring that all paths through the surveillance domain joining points in some start region S to some target region T will intersect the coverage region associated with at least one sensor. In this paper, we revisit a notion of redundant barrier coverage known as kbarrier coverage.
We describe two different notions of width, or impermeability, of the barrier provided by the sensors in $\cal A$ to paths joining two arbitrary regions S to T. The first, what we refer to as the thickness of the barrier, counts the minimum number of sensor region intersections, over all paths from S to T. The second, what we refer to as the resilience of the barrier, counts the minimum number of sensors whose removal permits a path from S to T with no sensor region intersections. Of course, a configuration of sensors with resilience k has thickness at least k and constitutes a kbarrier for S and T.
Our result demonstrates that any (Euclidean) shortest path from S to T that intersects a fixed number of distinct sensors, never intersects any one sensor more than three times. It follows that the resilience of $\cal A$ (with respect to S and T) is at least onethird the thickness of $\cal A$ (with respect to S and T). (Furthermore, if points in S and T are moderately separated (relative to the radius of individual sensor coverage) then no shortest path intersects any one sensor more than two times, and hence the resilience of $\cal A$ is at least onehalf the thickness of $\cal A$ .)
A second result, which we are only able to sketch here, shows that the approximation bounds can be tightened (to 1.666 in the case of moderately separated S and T) by exploiting topological properties of simple paths that make double visits to a collection of disks.
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 Title
 Approximating Barrier Resilience in Wireless Sensor Networks
 Book Title
 Algorithmic Aspects of Wireless Sensor Networks
 Book Subtitle
 5th International Workshop, ALGOSENSORS 2009, Rhodes, Greece, July 1011, 2009. Revised Selected Papers
 Pages
 pp 2940
 Copyright
 2009
 DOI
 10.1007/9783642054341_5
 Print ISBN
 9783642054334
 Online ISBN
 9783642054341
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 5804
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
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 Industry Sectors
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 Editors

 Shlomi Dolev ^{(16)}
 Editor Affiliations

 16. Department of Computer Science, Ben Gurion University of the Negev
 Authors

 Sergey Bereg ^{(17)}
 David Kirkpatrick ^{(18)}
 Author Affiliations

 17. Department of Computer Science, University of Texas at Dallas, USA
 18. Department of Computer Science, University of British Columbia, Canada
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