Approximating geometrical graphs via “spanners” and “banyans”
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Topology control and routing in ad hoc networks: a survey
ACM SIGACT News
Energy, congestion and dilation in radio networks
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Distributed Spanner with Bounded Degree for Wireless Ad Hoc Networks
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Distributed Maintenance of Resource Efficient Wireless Network Topologies (Distinguished Paper)
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Dynamic Data Structures for Realtime Management of Large Geormetric Scences (Extended Abstract)
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Geometric Searching in Walkthrough Animations with Weak Spanners in Real Time
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Geometric Spanners for Wireless Ad Hoc Networks
IEEE Transactions on Parallel and Distributed Systems
On local algorithms for topology control and routing in ad hoc networks
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Sparse Power Efficient Topology for Wireless Networks
HICSS '02 Proceedings of the 35th Annual Hawaii International Conference on System Sciences (HICSS'02)-Volume 9 - Volume 9
Congestion, Dilation, and Energy in Radio Networks
Theory of Computing Systems
Proceedings of the 2004 joint workshop on Foundations of mobile computing
Proceedings of the 2004 joint workshop on Foundations of mobile computing
Geometric spanners with applications in wireless networks
Computational Geometry: Theory and Applications
Studies on neighbourhood graphs for communication in multi agent systems
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
Performance analysis of the hierarchical layer graph for wireless networks
ADHOC-NOW'05 Proceedings of the 4th international conference on Ad-Hoc, Mobile, and Wireless Networks
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For c ∈ $\mathbb R$, a c-spanner is a subgraph of a complete Euclidean graph satisfying that between any two vertices there exists a path of weighted length at most c times their geometric distance Based on this property to approximate a complete weighted graph, sparse spanners have found many applications, e.g., in FPTAS, geometric searching, and radio networks In a weakc-spanner, this path may be arbitrary long but must remain within a disk of radius c-times the Euclidean distance between the vertices Finally in a c-power spanner, the total energy consumed on such a path, where the energy is given by the sum of the squares of the edge lengths on this path, must be at most c-times the square of the geometric distance of the direct link. While it is known that any c-spanner is also both a weak C1-spanner and a C2-power spanner (for appropriate C1,C2 depending only on c but not on the graph under consideration), we show that the converse fails: There exists a family of c1-power spanners that are no weak C-spanners and also a family of weak c2-spanners that are no C-spanners for any fixed C (and thus no uniform spanners, either) However the deepest result of the present work reveals that any weak spanner is also a uniform power spanner We further generalize the latter notion by considering (c,δ)-power spanners where the sum of the δ-th powers of the lengths has to be bounded; so (·,2)-power spanners coincide with the usual power spanners and (·,1)-power spanners are classical spanners Interestingly, these (·,δ)-power spanners form a strict hierarchy where the above results still hold for any δ ≥ 2; some even hold for δ 1 while counterexamples exist for δ d δ is no (C,δ)-power spanner for any fixed C, in general.