610,495 research outputs found
Distributed Algorithms for Maximizing the Lifetime of Wireless Sensor Networks
Wireless sensor networks (WSNs) are emerging as a key enabling technology for applications domains such as military, homeland security, and environment. However, a major constraint of these sensors is their limited battery. In this dissertation we examine the problem of maximizing the duration of time for which the network meets its coverage objective. Since these networks are very dense, only a subset of sensors need to be in sense or on mode at any given time to meet the coverage objective, while others can go into a power conserving sleep mode. This active set of sensors is known as a cover. The lifetime of the network can be extended by shuffling the cover set over time. In this dissertation, we introduce the concept of a local lifetime dependency graph consisting of the cover sets as nodes with any two nodes connected if the corresponding covers intersect, to capture the interdependencies among the covers. We present heuristics based on some simple properties of this graph and show how they improve over existing algorithms. We also present heuristics based on other properties of this graph, new models for dealing with the solution space and a generalization of our approach to other graph problems
Bounded-Angle Spanning Tree: Modeling Networks with Angular Constraints
We introduce a new structure for a set of points in the plane and an angle
, which is similar in flavor to a bounded-degree MST. We name this
structure -MST. Let be a set of points in the plane and let be an angle. An -ST of is a spanning tree of the
complete Euclidean graph induced by , with the additional property that for
each point , the smallest angle around containing all the edges
adjacent to is at most . An -MST of is then an
-ST of of minimum weight. For , an -ST does
not always exist, and, for , it always exists. In this paper,
we study the problem of computing an -MST for several common values of
.
Motivated by wireless networks, we formulate the problem in terms of
directional antennas. With each point , we associate a wedge of
angle and apex . The goal is to assign an orientation and a radius
to each wedge , such that the resulting graph is connected and its
MST is an -MST. (We draw an edge between and if , , and .) Unsurprisingly, the problem of computing an
-MST is NP-hard, at least for and . We
present constant-factor approximation algorithms for .
One of our major results is a surprising theorem for ,
which, besides being interesting from a geometric point of view, has important
applications. For example, the theorem guarantees that given any set of
points in the plane and any partitioning of the points into triplets,
one can orient the wedges of each triplet {\em independently}, such that the
graph induced by is connected. We apply the theorem to the {\em antenna
conversion} problem
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