20 research outputs found
Approximation Algorithm for Line Segment Coverage for Wireless Sensor Network
The coverage problem in wireless sensor networks deals with the problem of
covering a region or parts of it with sensors. In this paper, we address the
problem of covering a set of line segments in sensor networks. A line segment `
is said to be covered if it intersects the sensing regions of at least one
sensor distributed in that region. We show that the problem of finding the
minimum number of sensors needed to cover each member in a given set of line
segments in a rectangular area is NP-hard. Next, we propose a constant factor
approximation algorithm for the problem of covering a set of axis-parallel line
segments. We also show that a PTAS exists for this problem.Comment: 16 pages, 5 figures
An exercise in fault-containing: self-stabilizing leader election
Abstract Self-stabilizing algorithms are designed to guarantee convergence to some desired stable state from arbitrary initial states arising out of an arbitrarily large number of faults. However, in a well-designed system, the simultaneous occurrence of a large number of faults is rare. It is therefore desirable to design algorithms that are not only self-stabilizing, but also have the ability to recover very fast from a bounded number of faults. As an illustration, we present a simple self-stabilizing leader election protocol that recovers in 0( 1) time from a state with a single transient fault on oriented rings, Only the faulty node and its two neighbors change their state during convergence to a stable state. Thus, the effect of a single fault is tightly contained around the fault. The technique for transforming a self-stabilizing algorithm into its fault-contained version is simple and general, and can be applied to other problems as well that satisfy certain properties