There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
There are planar graphs almost as good as the complete graph
Journal of Computer and System Sciences
A sparse graph almost as good as the complete graph on points in K dimensions
Discrete & Computational Geometry
New sparseness results on graph spanners
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Wireless information networks
Balancing minimum spanning and shortest path trees
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Compact roundtrip routing for digraphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Compact roundtrip routing in directed networks (extended abstract)
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
Power consumption in packet radio networks
Theoretical Computer Science
A Distributed Algorithm for Minimum-Weight Spanning Trees
ACM Transactions on Programming Languages and Systems (TOPLAS)
Channel access scheduling in Ad Hoc networks with unidirectional links
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
Power optimization in routing protocols for wireless and mobile networks
Handbook of wireless networks and mobile computing
Roundtrip spanners and roundtrip routing in directed graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Mobile ad hoc networking and the IETF
ACM SIGMOBILE Mobile Computing and Communications Review
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
SIAM Journal on Computing
Distributed Spanner with Bounded Degree for Wireless Ad Hoc Networks
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Hardness Results for the Power Range Assignmet Problem in Packet Radio Networks
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Geometric Spanners for Wireless Ad Hoc Networks
IEEE Transactions on Parallel and Distributed Systems
Energy-efficient collision-free medium access control for wireless sensor networks
Proceedings of the 1st international conference on Embedded networked sensor systems
Compact roundtrip routing in directed networks
Journal of Algorithms
Fault-Tolerant Geometric Spanners
Discrete & Computational Geometry
Algorithmic aspects of topology control problems for ad hoc networks
Mobile Networks and Applications
A unified energy-efficient topology for unicast and broadcast
Proceedings of the 11th annual international conference on Mobile computing and networking
Fault-Tolerant Power Assignment and Backbone in Wireless Networks
PERCOMW '06 Proceedings of the 4th annual IEEE international conference on Pervasive Computing and Communications Workshops
Geometric spanners with applications in wireless networks
Computational Geometry: Theory and Applications
Computing a minimum-dilation spanning tree is NP-hard
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
Asymptotic critical total power for k-connectivity of wireless networks
IEEE/ACM Transactions on Networking (TON)
Power efficient resilience and lifetime in wireless ad-hoc networks
Proceedings of the 1st ACM international workshop on Foundations of wireless ad hoc and sensor networking and computing
On triangulations of a set of points in the plane
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Computing Lightweight Spanners Locally
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Reliable Key Establishment Scheme Exploiting Unidirectional Links in Wireless Sensor Networks
EUC '08 Proceedings of the 2008 IEEE/IFIP International Conference on Embedded and Ubiquitous Computing - Volume 01
Local Construction of Near-Optimal Power Spanners for Wireless Ad Hoc Networks
IEEE Transactions on Mobile Computing
Fault-tolerant spanners for general graphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Computing geometric minimum-dilation graphs is NP-hard
GD'06 Proceedings of the 14th international conference on Graph drawing
On spanners of geometric graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
The design space of wireless sensor networks
IEEE Wireless Communications
Improved multicriteria spanners for Ad-Hoc networks under energy and distance metrics
ACM Transactions on Sensor Networks (TOSN)
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In this paper, we study asymmetric power assignments that induce a low-energy k-strongly connected communication graph with spanner properties. We address two spanner models: energy and distance. The former serves as an indicator for the energy consumed in a message propagation between two nodes, while the latter reflects the geographic properties of routing in the induced communication graph. We consider a random wireless ad hoc network with |V| = n nodes distributed uniformly and independently in a unit square. For k ∈ {1,2}, we propose several power assignments that obtain a good bicriteria approximation on the total cost and stretch factor under the two models. For k 2, we analyze a power assignment developed by Carmi et al. and derive some interesting bounds on the stretch factor for both models as well. We also describe how to compute all the power assignments distributively, and we provide simulation results. To the best of our knowledge, these are the first provable theoretical bounds for low-cost spanners in wireless ad hoc networks.