A sparse graph almost as good as the complete graph on points in K dimensions
Discrete & Computational Geometry
GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
IEEE Transactions on Parallel and Distributed Systems
Routing with guaranteed delivery in ad hoc wireless networks
Wireless Networks
Topology control and routing in ad hoc networks: a survey
ACM SIGACT News
Online Routing in Triangulations
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Ad-hoc networks beyond unit disk graphs
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Navigating nets: simple algorithms for proximity search
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient Broadcasting and Gathering in Wireless Ad-Hoc Networks
ISPAN '05 Proceedings of the 8th International Symposium on Parallel Architectures,Algorithms and Networks
Searching dynamic point sets in spaces with bounded doubling dimension
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Localized topology control for heterogeneous wireless sensor networks
ACM Transactions on Sensor Networks (TOSN)
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
Mobile Networks and Applications
Geometric Spanner Networks
Efficient Delaunay-based localized routing for wireless sensor networks: Research Articles
International Journal of Communication Systems - Energy-Efficicent Network Protocols and Algorithms for Wireless Sensor Networks
Distributed proximity maintenance in ad hoc mobile networks
DCOSS'05 Proceedings of the First IEEE international conference on Distributed Computing in Sensor Systems
Geometric spanners for routing in mobile networks
IEEE Journal on Selected Areas in Communications
Localized Delaunay triangulation with application in ad hoc wireless networks
IEEE Transactions on Parallel and Distributed Systems
Spanners for geometric intersection graphs
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
The MST of symmetric disk graphs (in arbitrary metric spaces) is light
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
The MST of Symmetric Disk Graphs (in Arbitrary Metric Spaces) is Light
SIAM Journal on Discrete Mathematics
Improved multicriteria spanners for Ad-Hoc networks under energy and distance metrics
ACM Transactions on Sensor Networks (TOSN)
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This article presents an algorithm for constructing a spanner for ad hoc networks whose nodes have variable transmission range. Almost all previous spanner constructions for ad hoc networks assumed that all nodes in the network have the same transmission range. This allowed a succinct representation of the network as a unit disk graph, serving as the basis for the construction. In contrast, when nodes have variable transmission range, the ad hoc network must be modeled by a general disk graph. Whereas unit disk graphs are undirected, general disk graphs are directed. This complicates the construction of a spanner for the network, since currently there are no efficient constructions of low-stretch spanners for general directed graphs. Nevertheless, in this article it is shown that the class of disk graphs enjoys (efficiently constructible) spanners of quality similar to that of unit disk graph spanners. Moreover, it is shown that the new construction can be performed in a localized fashion. Our results use only simple packing arguments, hence all algorithms work for every metric space of constant doubling dimension.