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Sparse Fault-Tolerant Spanners for Doubling Metrics with Bounded Hop-Diameter or Degree

T.-H. Hubert Chan, Mingfei Li, Li Ning
2013 Algorithmica  
We study fault-tolerant spanners in doubling metrics.  ...  In addition, we also consider bounded hop-diameter, which is studied in the context of fault-tolerance for the first time even for Euclidean spanners.  ...  In this paper, we study fault-tolerant spanners for doubling metrics.  ... 
doi:10.1007/s00453-013-9779-y fatcat:nonqjlqdbveajfm5uwdt54jg6a

Sparse Fault-Tolerant Spanners for Doubling Metrics with Bounded Hop-Diameter or Degree [chapter]

T. -H. Hubert Chan, Mingfei Li, Li Ning
2012 Lecture Notes in Computer Science  
We study fault-tolerant spanners in doubling metrics.  ...  In addition, we also consider bounded hop-diameter, which is studied in the context of fault-tolerance for the first time even for Euclidean spanners.  ...  In this paper, we study fault-tolerant spanners for doubling metrics.  ... 
doi:10.1007/978-3-642-31594-7_16 fatcat:xo3ydhcivveo5jgamc7z5oopeq

Can't See the Forest for the Trees

Omri Kahalon, Hung Le, Lazar Milenković, Shay Solomon
2022 Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing  
We answer this question in the affirmative via a surprisingly simple observation on bounded hop-diameter spanners for tree metrics, which we apply on top of known, as well as new, tree cover theorems.  ...  Is it possible to efficiently navigate, on a sparse spanner, using 𝑘 hops and approximate distances, for 𝑘 close to 1 (say 𝑘 = 2)?  ...  ACKNOWLEDGMENTS The fourth-named author thanks Ofer Neiman for helpful discussions.  ... 
doi:10.1145/3519270.3538414 fatcat:oynmomltr5aqbdc56pi7fvfgla

Locality-Sensitive Orderings and Applications to Reliable Spanners [article]

Arnold Filtser, Hung Le
2022 arXiv   pre-print
We then construct such LSO's, as well as constructing considerably improved LSO's for doubling metrics.  ...  Along the way to the construction of LSO's and reliable spanners, we introduce and construct ultrametric covers, and construct 2-hop reliable spanners for the line.  ...  For vertex-fault-tolerant spanner, it was shown that every n-point set in R d , or more generally in a space of doubling dimension d, admits an f -vertex-fault-tolerant Luk99, Sol14] .  ... 
arXiv:2101.07428v3 fatcat:6iwemadvkncu7hgfwd2ym6fk3q

Can't See The Forest for the Trees: Navigating Metric Spaces by Bounded Hop-Diameter Spanners [article]

Omri Kahalon, Hung Le, Lazar Milenkovic, Shay Solomon
2022 arXiv   pre-print
To control the hop-length of paths, one can try to upper bound the spanner's hop-diameter, but naturally bounded hop-diameter spanners are more complex than spanners with unbounded hop-diameter, which  ...  The original metric enables us to navigate optimally – a single hop (for any two points) with the exact distance, but the price is high – Θ(n^2) edges. [...]  ...  Acknowledgments The fourth-named author thanks Ofer Neiman for helpful discussions.  ... 
arXiv:2107.14221v2 fatcat:dwdkmbygvzggvm5zz372xbalhm

Graph Spanners: A Tutorial Review [article]

Reyan Ahmed, Greg Bodwin, Faryad Darabi Sahneh, Keaton Hamm, Mohammad Javad Latifi Jebelli, Stephen Kobourov, Richard Spence
2020 arXiv   pre-print
As an additional contribution, we offer a list of open problems on graph spanners.  ...  This tutorial review provides a guiding reference to researchers who want to have an overview of the large body of literature about graph spanners.  ...  . . . . . . . . . . . . . . . . . . . . . . 51 11.10Spanners for Doubling Metrics . . . . . . . . . . . . . . . . . . . 52 12 Spanners For Changing Graphs 52 12.1 Fault Tolerant Spanners . . . . . . .  ... 
arXiv:1909.03152v2 fatcat:vqme4ewuvbbd5ac5erinyykwsy

Optimal Vertex Fault Tolerant Spanners (for fixed stretch) [chapter]

Greg Bodwin, Michael Dinitz, Merav Parter, Virginia Vassilevska Williams
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
greedy algorithm used to build spanners in the non-faulty setting. We also consider the edge fault tolerant (EFT) model, defined analogously with edge failures rather than vertex failures.  ...  Most notably, a landmark result of Althöfer et al. [3] proved that for any integer k ≥ 1, every graph G = (V, E) has a (2k − 1)-spanner H ⊆ G with O(n 1+1/k ) edges, and moreover, there exist graphs for  ...  Fault-tolerant approximate shortest-path trees. 19] T-H Hubert Chan, Mingfei Li, and Li Ning. Sparse fault-tolerant spanners for doubling metrics with bounded hop-diameter or degree.  ... 
doi:10.1137/1.9781611975031.123 dblp:conf/soda/BodwinDPW18 fatcat:t5sr4ib7freujfdjufj4sidzqe

Compact routing on euclidian metrics

Ittai Abraham, Dahlia Malkhi
2004 Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing - PODC '04  
Furthermore, our scheme is asymptotically optimal in Euclidean metrics whose diameter is polynomial. Compact Routing, Network Design. 1. Degree(H) -The maximal out going degree of H.  ...  Degree(H) = O(1). 2. M emory(RS) = O(log D). 3. Header(RS) = O(log D). 4. Stretch(RS) = 1 + ε. 5. Diameter(RS) = O(log D) with high probability.  ...  Acknowledgements The authors would like to thank Alex Samorodnitsky, Yair Bartal, and David Karger for useful discussions and the anonymous reviewers for their comments.  ... 
doi:10.1145/1011767.1011789 dblp:conf/podc/AbrahamM04 fatcat:vtk3c4g6ezew5jottep67yf7dm

Local Routing in a Tree Metric 1-Spanner [article]

Milutin Brankovic, Joachim Gudmundsson, André van Renssen
2021 arXiv   pre-print
This spanner has been applied in a series of papers devoted to designing bounded degree, low-diameter, low-weight (1+ϵ)-spanners in Euclidean and doubling metrics.  ...  The spanner has logarithmic lightness, logarithmic diameter, a linear number of edges and bounded degree (provided the input tree has bounded degree).  ...  We have also shown that this algorithm can be used to route in a spanner for doubling metrics which uses the shortcutting scheme to achieve a low diameter while maintaining low weight and low degree.  ... 
arXiv:2012.00959v2 fatcat:eso5b6shqzcplbkacj3cjupnji

Applications of k-local MST for topology control and broadcasting in wireless ad hoc networks

Xiang-Yang Li, Yu Wang, Wen-Zhan Song
2004 IEEE Transactions on Parallel and Distributed Systems  
They proved that the final graph, called local minimum spanning tree (LMST), is connected, and has a bounded degree 6.  ...  The best distributed algorithm [12] can compute MST in O(n) rounds using O(m + n log n) communications for a general graph with m edges and n nodes.  ...  We have shown that we can construct a bounded degree planar spanner, or a bounded degree planar low-weighted structure, or a bounded degree k-fault tolerant spanner, or a bounded degree fault tolerant  ... 
doi:10.1109/tpds.2004.77 fatcat:52vwu4jxzvhj7ddz4sikvnn74i

Three-dimensional ocean sensor networks: A survey

Yu Wang, Yingjian Liu, Zhongwen Guo
2012 Journal of Ocean University of China  
In this paper, we aim to provide an overview of the most recent advances in network design principles for 3D ocean sensor networks, with focuses on deployment, localization, topology design, and position-based  ...  The past decade has seen a growing interest in ocean sensor networks because of their wide applications in marine research, oceanography, ocean monitoring, offshore exploration, and defense or homeland  ...  To achieve both sparseness and fault tolerance, extended 3D RNG, 3D GG, and 3D Yao structures to support fault tolerance by a simple modification of their definitions.  ... 
doi:10.1007/s11802-012-2111-7 fatcat:czpva2smgng43hsgmc3cd5hcim

Treewidth and Hyperbolicity of the Internet

Fabien de Montgolfier, Mauricio Soto, Laurent Viennot
2011 2011 IEEE 10th International Symposium on Network Computing and Applications  
Additionally, we compute the treewidth and hyperbolicity obtained for classical Internet models and compare with the snapshots.  ...  On the one hand, the treewidth of the Internet appears to be quite large and being far from a tree with that respect, reflecting some high degree of connectivity.  ...  example of sparse graph with high treewidth).  ... 
doi:10.1109/nca.2011.11 dblp:conf/nca/MontgolfierSV11 fatcat:mo76tsvokfhl3bbh6duh4ov7mu

06481 Abstracts Collection – Geometric Networks and Metric Space Embeddings

Joachim Gudmundsson, Rolf Klein, Giri Narasimhan, Michiel Smid, Alexander Wolff
2007
Links to extended abstracts or full papers are provided where available.  ...  The Dagstuhl Seminar 06481 "Geometric Networks and Metric Space Embeddings" was held from November~26 to December~1, 2006 in the International Conference and Research Center (IBFI), Schloss Dagstuhl.  ...  We consider the problem of constructing sparse (1 + ε)-spanners with small hop diameter for metrics of low doubling dimension.  ... 
doi:10.4230/dagsemproc.06481.1 fatcat:26vlteaiuzewrhxw7bs5uuk6m4

Reliable Spanners: Locality-Sensitive Orderings Strike Back [article]

Arnold Filtser, Hung Le
2021
We then construct such LSO's, as well as constructing considerably improved LSO's for doubling metrics.  ...  Along the way to the construction of LSO's and reliable spanners, we introduce and construct ultrametric covers, and construct $2$-hop reliable spanners for the line.  ...  For vertex-fault-tolerant spanner, it was shown that every n-point set in R d , or more generally in a space of doubling dimension d, admits an f -vertex-fault-tolerant Luk99, Sol14] .  ... 
doi:10.48550/arxiv.2101.07428 fatcat:fyjgmkd35vfpngm5jeq56eyhqy

Reliable Spanners for Metric Spaces

Sariel Har-Peled, Manor Mendel, Dániel Oláh, Kevin Buchin, Éric Colin de Verdière
2021
Here, we present new constructions of reliable spanners for planar graphs, trees and (general) metric spaces.  ...  More precisely, any failure of some nodes can only cause a small damage in the remaining graph in terms of the dilation, that is, the spanner property is maintained for almost all nodes in the residual  ...  A graph G is a k-fault tolerant t-spanner, if for any subset of vertices B, with |B| ď k, the graph GzB is a t-spanner.  ... 
doi:10.4230/lipics.socg.2021.43 fatcat:kjzdcwverzclzomfzj6yrqacnu
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