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Improved Purely Additive Fault-Tolerant Spanners [article]

Davide Bilò, Fabrizio Grandoni, Luciano Gualà, Stefano Leucci, Guido Proietti
2015 arXiv   pre-print
We also obtain improved fault-tolerant additive spanners for the case of one vertex failure, and for the case of f edge failures.  ...  In this paper, we focus on fault-tolerant additive spanners, namely additive spanners which are able to preserve their additive stretch even when one edge fails.  ...  Augmenting Sourcewise Fault-Tolerant Spanners We next describe a general procedure (see Algorithm 1) to derive purely additive fault-tolerant spanners from sourcewise spanners of the same type.  ... 
arXiv:1507.00505v1 fatcat:4egrechb3ve4fhv6mez3p7zunm

Improved Purely Additive Fault-Tolerant Spanners [chapter]

Davide Bilò, Fabrizio Grandoni, Luciano Gualà, Stefano Leucci, Guido Proietti
2015 Lecture Notes in Computer Science  
We also obtain improved fault-tolerant additive spanners for the case of one vertex failure, and for the case of f edge failures.  ...  In this paper, we focus on fault-tolerant additive spanners, namely additive spanners which are able to preserve their additive stretch even when one edge fails.  ...  Augmenting Sourcewise Fault-Tolerant Spanners We next describe a general procedure (see Algorithm 1) to derive purely additive fault-tolerant spanners from sourcewise spanners of the same type.  ... 
doi:10.1007/978-3-662-48350-3_15 fatcat:lqwrqjtwfvbtfehw7hjnsttu7i

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.  ...  which this size-stretch tradeoff cannot be improved (if we assume the girth conjecture of Erdős [29]).  ...  Construction of purely additive fault tolerant spanners were studied in [17, 11, 15] .  ... 
doi:10.1137/1.9781611975031.123 dblp:conf/soda/BodwinDPW18 fatcat:t5sr4ib7freujfdjufj4sidzqe

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.  ...  [50] study additive and linear fault tolerant spanners.  ... 
arXiv:1909.03152v2 fatcat:vqme4ewuvbbd5ac5erinyykwsy

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

Greg Bodwin, Michael Dinitz, Merav Parter, Virginia Vassilevska Williams
2017 arXiv   pre-print
A subgraph H ⊆ G is an f vertex fault tolerant (VFT) k-spanner if H ∖ F is a k-spanner of G ∖ F for any small set F of f vertices that might "fail."  ...  One of the main questions in the area is: what is the minimum size of an f fault tolerant k-spanner that holds for all n node graphs (as a function of f, k and n)?  ...  Construction of purely additive fault tolerant spanners were studied in [16, 10, 14] .  ... 
arXiv:1710.03164v1 fatcat:wbl2z7avyzcvbiuntbk4xfles4

Partially Optimal Edge Fault-Tolerant Spanners [article]

Greg Bodwin, Michael Dinitz, Caleb Robelle
2021 arXiv   pre-print
Our proof is an analysis of the fault-tolerant greedy algorithm, which requires exponential time, but we also show that there is a polynomial-time algorithm which creates edge fault tolerant spanners that  ...  Our main result is to nearly close this gap with an improved upper bound, thus separating the cases of edge and vertex faults.  ...  So the main open question left is how to close this gap: how much extra do we have to pay to achieve edge fault tolerance compared to a non-fault tolerant spanner?  ... 
arXiv:2102.11360v1 fatcat:v6ynaybjlfc6pcvh4h6zqst7ki

Incubators vs Zombies: Fault-Tolerant, Short, Thin and Lanky Spanners for Doubling Metrics [article]

T-H. Hubert Chan, Mingfei Li, Li Ning
2012 arXiv   pre-print
Indeed, our approach can be readily applied to our previous construction of k-fault tolerant spanners (ICALP 2012) to achieve k-fault tolerance, maximum degree O(k^2), hop-diameter O(log n) and lightness  ...  Recently Elkin and Solomon gave a construction of spanners for doubling metrics that has constant maximum degree, hop-diameter O(log n) and lightness O(log n) (i.e., weight O(log n)w(MST).  ...  Then, we show that H is a k-fault-tolerant (1 + )-spanner for X.  ... 
arXiv:1207.0892v1 fatcat:27wbzk6abvbtdkq3b6xzymxwfy

Vertex Fault-Tolerant Emulators [article]

Greg Bodwin, Michael Dinitz, Yasamin Nazari
2021 arXiv   pre-print
We also show constructions of fault-tolerant emulators with additive error, demonstrating that these also enjoy significantly improved tradeoffs over those available for fault-tolerant additive spanners  ...  That is: we introduce a natural definition of vertex fault-tolerant emulators, and then we show a three-way tradeoff between size, stretch, and fault-tolerance for these emulators that polynomially surpasses  ...  In other words, tolerating one additional fault costs poly(n) in spanner size, and there is no way to tolerate Ω(log n) faults in subquadratic size.  ... 
arXiv:2109.08042v2 fatcat:v7gszyn2lbajxg7h3wpljs56gy

On Resilient Graph Spanners [article]

G. Ausiello, P. G. Franciosa, G. F. Italiano, A. Ribichini
2014 arXiv   pre-print
We introduce and investigate a new notion of resilience in graph spanners. Let S be a spanner of a graph G.  ...  In this paper we show that sparse resilient spanners exist, and that they can be computed efficiently.  ...  under edge additions: for example, if S is fault-tolerant then R is fault-tolerant too.  ... 
arXiv:1303.1559v4 fatcat:gwrgfqmz2zfe5mek4tyankwe24

Improved Dynamic Graph Learning through Fault-Tolerant Sparsification

Chun Jiang Zhu, Sabine Storandt, Kam-yiu Lam, Song Han, Jinbo Bi
2019 International Conference on Machine Learning  
We propose a new type of graph sparsification namely fault-tolerant (FT) sparsification to significantly reduce the cost to only a constant.  ...  In addition, FT spectral sparsification can be generalized to FT cut sparsification, for cut-based graph learning.  ...  For short, we will use VFT and EFT to refer to Vertex-Fault-Tolerant and Edge-Fault-Tolerant, respectively. f -VFT (f -EFT) kspanners are a subgraph such that for all vertex (edge) faults of size at most  ... 
dblp:conf/icml/ZhuSLHB19 fatcat:dfazlo5zhjf4vouy7az3qzsh2e

From Google File System to Omega: A Decade of Advancement in Big Data Management at Google

Jade Yang
2015 2015 IEEE First International Conference on Big Data Computing Service and Applications  
The study article examines ten major milestone papers on big data management published by Google, from Google File system (GFS), MapReduce, Bigtable, Chubby, Percolator, Pregel, Dremel, to Megastore, Spanner  ...  First of all, high fault tolerance is an integral part of all Google projects.  ...  For fault tolerance, operation logs which contain a record of metadata changes are stored on the master's local disk.  ... 
doi:10.1109/bigdataservice.2015.47 dblp:conf/bigdataservice/Yang15 fatcat:hjthmevg7beblisdrdswxxnv7q

A Model and Survey of Distributed Data-Intensive Systems [article]

Alessandro Margara, Gianpaolo Cugola, Nicolò Felicioni, Stefano Cilloni
2022 arXiv   pre-print
Each data-intensive system brings its specific choices in terms of data model, usage assumptions, synchronization, processing strategy, deployment, guarantees in terms of consistency, fault tolerance,  ...  As an additional fault tolerance mechanism, B-trees and logs are periodically checkpointed to durable storage.  ...  Fault tolerance Fault tolerance is the ability of a system to tolerate failures that may occur during its execution.  ... 
arXiv:2203.10836v1 fatcat:xbg34nuzhndwjpv2asbbhtgvlu

Rumor Spreading with No Dependence on Conductance

Keren Censor-Hillel, Bernhard Haeupler, Jonathan Kelner, Petar Maymounkov
2017 SIAM journal on computing (Print)  
Combining the faster NeighborExchange of [28] with the the spanner and simulator  ...  This is at most an additive polylogarithmic factor from the trivial lower bound of D.  ...  We thank the reviewers for many comments and suggestions that helped us to improve the paper.  ... 
doi:10.1137/14099992x fatcat:gm7epgi5ovc6bkqjqrzabrxpqi

Approximation Schemes for Minimum 2-Connected Spanning Subgraphs in Weighted Planar Graphs [chapter]

André Berger, Artur Czumaj, Michelangelo Grigni, Hairong Zhao
2005 Lecture Notes in Computer Science  
Then we present a new greedy spanner construction for edge-weighted planar graphs, which augments any connected subgraph A of a weighted planar graph G to a (1 + ε)-spanner of G with total weight bounded  ...  Naturally, one may think to use light fault-tolerant spanners (see, e.g., in [20] ), which are subgraphs that persist as s-spanners even after deleting a constant number of vertices or edges.  ...  Unfortunately, this concept is not useful in our setting, since simple examples show that light fault-tolerant spanners do not exist in weighted planar graphs, not even for a single edge deletion.  ... 
doi:10.1007/11561071_43 fatcat:m565l4ypivaafiuyt6vvzq5goe

Consus: Taming the Paxi [article]

Robert Escriva, Robbert van Renesse
2016 arXiv   pre-print
Spanner and Replicated Commit Spanner [1] implements a classic 2-phase commit protocol where all participants to the protocol are made fault tolerant using Multi-Paxos.  ...  Practically, this means that Consus is more conservative in its approach to data handling, opting to log data to disk rather than rely purely upon replication for fault tolerance.  ... 
arXiv:1612.03457v1 fatcat:hbqq7ph775d6tayvej7wmlmm2i
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