Delaunay graphs are almost as good as complete graphs
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
Robust position-based routing in wireless Ad Hoc networks with unstable transmission ranges
DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
Geometric spanner for routing in mobile networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
Routing with guaranteed delivery in ad hoc wireless networks
Wireless Networks
Message-optimal connected dominating sets in mobile ad hoc networks
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
On the Spanning Ratio of Gabriel Graphs and beta-skeletons
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Worst-Case optimal and average-case efficient geometric ad-hoc routing
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
Geometric ad-hoc routing: of theory and practice
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Ad-hoc networks beyond unit disk graphs
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Minimizing interference in ad hoc and sensor networks
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
On the pitfalls of geographic face routing
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
A unified energy-efficient topology for unicast and broadcast
Proceedings of the 11th annual international conference on Mobile computing and networking
Local approximation schemes for topology control
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Lazy cross-link removal for geographic routing
Proceedings of the 4th international conference on Embedded networked sensor systems
Echo Algorithms: Depth Parallel Operations on General Graphs
IEEE Transactions on Software Engineering
A local distributed algorithm to approximate MST in unit disc graphs
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Separability and topology control of quasi unit disk graphs
Wireless Networks
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We present a distributed topology control protocol that runs on a d-QUDG for d ≥ 1/√2, and computes a sparse, constant-spanner, both in Euclidean distance and in hop distance. QUDGs (short for Quasi Unit Disk Graphs) generalize Unit Disk Graphs and permit more realistic modeling of wireless networks, allowing for imperfect and non-uniform transmission ranges as well as uncertain node location information. Our protocol is local and runs in O(1) rounds. The output topology permits memoryless (geographic) routing with guaranteed delivery. In fact, when our topology control protocol is used as preprocessing step for the geographic routing protocol GOAFR+ we get the routing time guarantee of O(l2) for any source-destination pair that are lunits away from each other in the input d-QUDG. The key idea is simple: to obtain planarity, we replace each edge intersection with a virtual node and have a real node serve as a proxy for the virtual node. This idea is supported by other parts of our protocol that (i) use clustering to keep the density of edge crossings bounded and (ii) guarantee that an edge between a virtual node and a neighbor is realized by a constant-hop path in the real network. The virtual node idea is simple enough to be useful in many contexts. For example, it can be combined with a scheme recently suggested by Funke and Milosavljevic (INFOCOM 2007) to guarantee delivery under uncertain node locations. Similarly, the virtual nodes idea can also be used as a cheap alternative to edge-crossing removal schemes suggested by Kim et al. (DIALM-POMC 2005, SENSYS 2006).