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Approximation Algorithms for Computing Minimum Exposure Paths in a Sensor Field
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DOI：10.1145/1807048.1807052.png)
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Abstract
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The exposure of a path p in a sensor field is a measure of the likelihood that an object traveling along p is detected by at least one sensor from a network of sensors, and is formally defined as an integral over all points x of p of the sensibility (the strength of the signal coming from x) times the element of path length. The minimum exposure path (MEP) problem is, given a pair of points x and y inside a sensor field, to find a path between x and y of minimum exposure. In this article we introduce the first rigorous treatment of the problem, designing an approximation algorithm for the MEP problem with guaranteed performance characteristics. Given a convex polygon P of size n with O(n) sensors inside it and any real number epsilon > 0, our algorithm finds a path in P whose exposure is within an 1 + epsilon factor of the exposure of the MEP, in time O(n/epsilon(2)psi log n), where. is a geometric characteristic of the field. We also describe a framework for a faster implementation of our algorithm, which reduces the time by a factor of approximately Theta(1/epsilon), while keeping the same approximation ratio.
Keywords:
Algorithms
Performance
Theory
Sensor networks
minimum exposure paths
coverage
approximation algorithms
shortest paths
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