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Improved Algorithms for Constructing Fault-Tolerant Spanners

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)? ...

##
###
Fault Tolerant Additive Spanners
[chapter]

2012
*
Lecture Notes in Computer Science
*

This allows us to derive a poly-time

doi:10.1007/978-3-642-34611-8_22
fatcat:wxamc2w57jhb7lby5mft7m2uum
*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 ...##
###
A Polynomial Time Algorithm for Almost Optimal Vertex Fault Tolerant Spanners
[article]

2020
*
arXiv
*
pre-print

Prior to this work, no other polynomial time

arXiv:2002.11617v2
fatcat:3h5d4yfn4zdyfkqdctqzle6ij4
*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. ...##
###
A Trivial Yet Optimal Solution to Vertex Fault Tolerant Spanners
[article]

2019
*
arXiv
*
pre-print

We give a short and easy upper bound on the worst-case size of

arXiv:1812.05778v2
fatcat:6kvbggqzhfgwnfo73y3qtdbpsu
*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 . ...##
###
Fault-tolerant spanners

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*. ...

##
###
Fault-Tolerant Spanners: Better and Simpler
[article]

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*...

##
###
Improved Purely Additive Fault-Tolerant Spanners
[chapter]

2015
*
Lecture Notes in Computer Science
*

We also obtain

doi:10.1007/978-3-662-48350-3_15
fatcat:lqwrqjtwfvbtfehw7hjnsttu7i
*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*. ...##
###
Optimal Vertex Fault-Tolerant Spanners in Polynomial Time
[article]

2020
*
arXiv
*
pre-print

This reflects an exponential

arXiv:2007.08401v3
fatcat:zev6ip3clnb2rcjfl5vaoooqgu
*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. ...##
###
Fault-tolerant geometric spanners

2003
*
Proceedings of the nineteenth conference on Computational geometry - SCG '03
*

Our next contribution is an efficient

doi:10.1145/777792.777794
dblp:conf/compgeom/CzumajZ03
fatcat:nfcyhnasnbaw5gd6yyuee3kfci
*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*. ...##
###
Fault-Tolerant Geometric Spanners

2004
*
Discrete & Computational Geometry
*

Our next contribution is an efficient

doi:10.1007/s00454-004-1121-7
fatcat:kjro72dnfjb65mfegebd7mnaiy
*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*. ...##
###
Fault-tolerant geometric spanners

2003
*
Proceedings of the nineteenth conference on Computational geometry - SCG '03
*

Our next contribution is an efficient

doi:10.1145/777793.777794
fatcat:lakbayrac5bsrhckiargyrr3re
*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*. ...##
###
Fault Tolerant Spanners for General Graphs

2010
*
SIAM journal on computing (Print)
*

It is known how to efficiently

doi:10.1137/090758039
fatcat:7pwpjwfehzgw7bidj7zt3x5u2e
*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*. ...##
###
Fault-tolerant spanners for general graphs

2009
*
Proceedings of the 41st annual ACM symposium on Symposium on theory of computing - STOC '09
*

It is known how to efficiently

doi:10.1145/1536414.1536475
dblp:conf/stoc/ChechikLPR09
fatcat:xq7bxdormjahfftlq2qahl42ie
*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*. ...##
###
Fault-Tolerant Logical Network Structures

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

dblp:journals/eatcs/Parter16
fatcat:b367phvhmbe7riq4qkixr26tsi
*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 ...##
###
Efficient and Simple Algorithms for Fault Tolerant Spanners
[article]

2020
*
arXiv
*
pre-print

It was recently shown that a version of the greedy

arXiv:2002.10889v2
fatcat:sukfh5qemnhhxfjfy5khyc2tgi
*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. ...
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