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Improved Algorithms for Constructing Fault-Tolerant Spanners

Levcopoulos, Narasimhan, Smid
2002 Algorithmica  
Algorithms are given that construct k-fault-tolerant spanners for S.  ...  First, an algorithm is given that transforms an arbitrary spanner into a k-fault-tolerant spanner.  ...  Can such a fault-tolerant spanner be constructed in time O(n log n + kn)?  ... 
doi:10.1007/s00453-001-0075-x fatcat:tbsvmefucbevpoijwnabjmj2fq

Fault Tolerant Additive Spanners [chapter]

Gilad Braunschvig, Shiri Chechik, David Peleg
2012 Lecture Notes in Computer Science  
This allows us to derive a poly-time algorithm Span f −t add for constructing an additive fault tolerant spanner H of G, relying on the existence of algorithms for constructing fault tolerant multiplicative  ...  Recently, the problem of constructing fault-tolerant multiplicative spanners for general graphs was given some algorithms.  ...  Constructions for multiplicative fault tolerant spanners for general graphs that are robust to edge or vertex failures were presented in [5] , later the construction for vertex failures was improved in  ... 
doi:10.1007/978-3-642-34611-8_22 fatcat:wxamc2w57jhb7lby5mft7m2uum

A Polynomial Time Algorithm for Almost Optimal Vertex Fault Tolerant Spanners [article]

Udit Agarwal
2020 arXiv   pre-print
Prior to this work, no other polynomial time algorithm was known for constructing f vertex fault tolerant spanner with optimal size.  ...  Our algorithm for constructing f vertex fault tolerant spanner takes O(k· n· m^2 · W) time, where W is the maximum edge weight, and constructs a spanner of size O(n^1+1/kf^1-1/k· (log n)^1-1/k).  ...  This is the first work that presents a polynomial time algorithm for constructing f vertex fault tolerant spanners for integer edge weights.  ... 
arXiv:2002.11617v2 fatcat:3h5d4yfn4zdyfkqdctqzle6ij4

A Trivial Yet Optimal Solution to Vertex Fault Tolerant Spanners [article]

Greg Bodwin, Shyamal Patel
2019 arXiv   pre-print
We give a short and easy upper bound on the worst-case size of fault tolerant spanners, which improves on all prior work and is fully optimal at least in the setting of vertex faults.  ...  A spanner for such a system needs to be robust to these failures, giving rise to the notion of fault tolerance: Definition 2 (Fault Tolerant Spanners).  ...  Edge Fault Tolerant (EFT), k-spanner of G if for any set of F vertices (resp. edges) in G of size |F | ≤ f , H \ F is a k-spanner of G \ F .  ... 
arXiv:1812.05778v2 fatcat:6kvbggqzhfgwnfo73y3qtdbpsu

Fault-tolerant spanners

Michael Dinitz, Robert Krauthgamer
2011 Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '11  
For stretch k ≥ 3 we design a simple transformation that converts every k-spanner construction with at most f (n) edges into an r-fault-tolerant k-spanner construction with at most O(r 3 log n) · f (2n  ...  In this paper we examine spanners of general graphs that are tolerant to vertex failures, and significantly improve their dependence on the number of faults r for all stretch bounds.  ...  Algorithm 1: Rounding algorithm for r-fault tolerant 2-spanner.  ... 
doi:10.1145/1993806.1993830 dblp:conf/podc/DinitzK11 fatcat:sdqewsrhczfk7bd3nqwteit7le

Fault-Tolerant Spanners: Better and Simpler [article]

Michael Dinitz, Robert Krauthgamer
2011 arXiv   pre-print
For stretch k ≥ 3 we design a simple transformation that converts every k-spanner construction with at most f(n) edges into an r-fault-tolerant k-spanner construction with at most O(r^3 n) · f(2n/r) edges  ...  In this paper we examine spanners of general graphs that are tolerant to vertex failures, and significantly improve their dependence on the number of faults r, for all stretch bounds.  ...  In fact, we prove something slightly stronger: a general conversion theorem that turns any algorithm for constructing k-spanners with size f (n) into an algorithm for constructing r-fault tolerant k-spanners  ... 
arXiv:1101.5753v1 fatcat:ddpsog65nnculagpn4sd2utzbu

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.  ...  On the other hand, we show how to augment some known fault-tolerant additive spanners, based on clustering techniques.  ...  Algorithm 2: Algorithm for computing a fault-tolerant additive spanner from multiplicative and clustering-based additive spanners.  ... 
doi:10.1007/978-3-662-48350-3_15 fatcat:lqwrqjtwfvbtfehw7hjnsttu7i

Optimal Vertex Fault-Tolerant Spanners in Polynomial Time [article]

Greg Bodwin, Michael Dinitz, Caleb Robelle
2020 arXiv   pre-print
This reflects an exponential improvement in runtime over [Bodwin-Patel PODC '19], the only previously known algorithm for constructing optimal vertex fault-tolerant spanners.  ...  Recent work has pinned down the existentially optimal size bounds for vertex fault-tolerant spanners: for any positive integer k, every n-node graph has a (2k-1)-spanner on O(f^1-1/k n^1+1/k) edges resilient  ...  Acknowledgements We would like to thank Xin Li for many helpful discussions about derandomization, and in particular for pointing us towards message authentication codes.  ... 
arXiv:2007.08401v3 fatcat:zev6ip3clnb2rcjfl5vaoooqgu

Fault-tolerant geometric spanners

Artur Czumaj, Hairong Zhao
2003 Proceedings of the nineteenth conference on Computational geometry - SCG '03  
Our next contribution is an efficient algorithm for constructing good fault-tolerant spanners. We present a new, sufficient condition for a graph to be a k-fault-tolerant spanner.  ...  We present a greedy algorithm that for any t > 1 and any non-negative integer k, constructs a k-fault-tolerant t-spanner in which every vertex is of degree O(k) and whose total cost is O(k 2 ) times the  ...  They presented in [17] three algorithms constructing k-vertex fault-tolerant spanners.  ... 
doi:10.1145/777792.777794 dblp:conf/compgeom/CzumajZ03 fatcat:nfcyhnasnbaw5gd6yyuee3kfci

Fault-Tolerant Geometric Spanners

Artur Czumaj, Hairong Zhao
2004 Discrete & Computational Geometry  
Our next contribution is an efficient algorithm for constructing good fault-tolerant spanners. We present a new, sufficient condition for a graph to be a k-fault-tolerant spanner.  ...  We present a greedy algorithm that for any t > 1 and any non-negative integer k, constructs a k-fault-tolerant t-spanner in which every vertex is of degree O(k) and whose total cost is O(k 2 ) times the  ...  They presented in [17] three algorithms constructing k-vertex fault-tolerant spanners.  ... 
doi:10.1007/s00454-004-1121-7 fatcat:kjro72dnfjb65mfegebd7mnaiy

Fault-tolerant geometric spanners

Artur Czumaj, Hairong Zhao
2003 Proceedings of the nineteenth conference on Computational geometry - SCG '03  
Our next contribution is an efficient algorithm for constructing good fault-tolerant spanners. We present a new, sufficient condition for a graph to be a k-fault-tolerant spanner.  ...  We present a greedy algorithm that for any t > 1 and any non-negative integer k, constructs a k-fault-tolerant t-spanner in which every vertex is of degree O(k) and whose total cost is O(k 2 ) times the  ...  They presented in [17] three algorithms constructing k-vertex fault-tolerant spanners.  ... 
doi:10.1145/777793.777794 fatcat:lakbayrac5bsrhckiargyrr3re

Fault Tolerant Spanners for General Graphs

S. Chechik, M. Langberg, D. Peleg, L. Roditty
2010 SIAM journal on computing (Print)  
It is known how to efficiently construct a (2k −1)-spanner of size O(n 1+1/k ), and this sizestretch tradeoff is conjectured to be tight.  ...  The paper concerns graph spanners that are resistant to vertex or edge failures.  ...  VERTEX FAULT TOLERANT SPANNER In this section we present the main result of this paper, an algorithm for constructing an f -vertex fault tolerant spanner.  ... 
doi:10.1137/090758039 fatcat:7pwpjwfehzgw7bidj7zt3x5u2e

Fault-tolerant spanners for general graphs

S. Chechik, M. Langberg, David Peleg, L. Roditty
2009 Proceedings of the 41st annual ACM symposium on Symposium on theory of computing - STOC '09  
It is known how to efficiently construct a (2k −1)-spanner of size O(n 1+1/k ), and this sizestretch tradeoff is conjectured to be tight.  ...  The paper concerns graph spanners that are resistant to vertex or edge failures.  ...  VERTEX FAULT TOLERANT SPANNER In this section we present the main result of this paper, an algorithm for constructing an f -vertex fault tolerant spanner.  ... 
doi:10.1145/1536414.1536475 dblp:conf/stoc/ChechikLPR09 fatcat:xq7bxdormjahfftlq2qahl42ie

Fault-Tolerant Logical Network Structures

Merav Parter
2016 Bulletin of the European Association for Theoretical Computer Science  
We hope that this would pave the way towards the development of a more generalized theory for the design of fault-tolerant networks.  ...  Fault-Tolerant (FT) Logical Network Structures are low cost high resilient structures, constructed on top of a given network, that satisfy certain desirable performance requirements concerning, e.g., connectivity  ...  One of the most basic FT-structures that calls for a lower bound construction is fault-tolerant additive spanners, namely, subraphs that provide an additive approximation for all pairs distances in presence  ... 
dblp:journals/eatcs/Parter16 fatcat:b367phvhmbe7riq4qkixr26tsi

Efficient and Simple Algorithms for Fault Tolerant Spanners [article]

Michael Dinitz, Caleb Robelle
2020 arXiv   pre-print
It was recently shown that a version of the greedy algorithm gives a construction of fault-tolerant spanners that is size-optimal, at least for vertex faults.  ...  Designing a polynomial-time algorithm to construct (near-)optimal fault-tolerant spanners was given as an explicit open problem in the two most recent papers on fault-tolerant spanners ([Bodwin, Dinitz  ...  The original greedy algorithm for fault-tolerant spanners was introduced and analyzed by [BDPW18] , with an improved analysis by [BP19] , and is given in Algorithm 1.  ... 
arXiv:2002.10889v2 fatcat:sukfh5qemnhhxfjfy5khyc2tgi
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