Discrete Mathematics - Topics on domination
The Cricket location-support system
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
Probability and statistics with reliability, queuing and computer science applications
Probability and statistics with reliability, queuing and computer science applications
Introduction to Algorithms
Random channel assignment in the plane
Random Structures & Algorithms
Localization from mere connectivity
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
Range-free localization schemes for large scale sensor networks
Proceedings of the 9th annual international conference on Mobile computing and networking
Localization for mobile sensor networks
Proceedings of the 10th annual international conference on Mobile computing and networking
Robust distributed network localization with noisy range measurements
SenSys '04 Proceedings of the 2nd international conference on Embedded networked sensor systems
Graph Theory With Applications
Graph Theory With Applications
A Theory of Network Localization
IEEE Transactions on Mobile Computing
Journal of Computational and Applied Mathematics
The design space of wireless sensor networks
IEEE Wireless Communications
Proceedings of the 5th ACM workshop on Performance monitoring and measurement of heterogeneous wireless and wired networks
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When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph, defined to be the number of edges on a shortest path between them. In this paper, we consider a network of sensors placed uniformly at random in a two-dimensional region and study two conditional distributions related to these distances. The first is the probability distribution of distances in the graph, conditioned on Euclidean distances; the other is the probability density function associated with Euclidean distances, conditioned on distances in the graph. We study these distributions both analytically (when feasible) and by means of simulations. To the best of our knowledge, our results constitute the first of their kind and open up the possibility of discovering improved solutions to certain sensor-network problems, as for example sensor localization.