An optimal synchronizer for the hypercube
SIAM Journal on Computing
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Journal of Algorithms
Online tracking of mobile users
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Randomized algorithms
Efficient algorithms for constructing fault-tolerant geometric spanners
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
New Results of Fault Tolerant Geometric Spanners
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Fault-tolerant geometric spanners
Proceedings of the nineteenth annual symposium on Computational geometry
The intrinsic dimensionality of graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Journal of the ACM (JACM)
The price of being near-sighted
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
On the locality of distributed sparse spanner construction
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
SIAM Journal on Computing
Fault-tolerant spanners for general graphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Concentration of Measure for the Analysis of Randomized Algorithms
Concentration of Measure for the Analysis of Randomized Algorithms
A constructive proof of the general lovász local lemma
Journal of the ACM (JACM)
Replacement Paths via Fast Matrix Multiplication
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Directed spanners via flow-based linear programs
Proceedings of the forty-third annual ACM symposium on Theory of computing
Directed spanners via flow-based linear programs
Proceedings of the forty-third annual ACM symposium on Theory of computing
Sparse fault-tolerant spanners for doubling metrics with bounded hop-diameter or degree
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Fault tolerant additive spanners
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Multipath spanners via fault-tolerant spanners
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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A natural requirement for many distributed structures is fault-tolerance: after some failures in the underlying network, whatever remains from the structure should still be effective for whatever remains from the network. 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. For stretch k e 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(r3 log n) Å f(2n/r) edges. Applying this to standard greedy spanner constructions gives r-fault tolerant k-spanners with Õ(r2 n1+2/k+1) edges. The previous construction by Chechik, Langberg, Peleg, and Roddity [STOC 2009] depends similarly on n but exponentially on r (approximately like kr). For the case of k=2 and unit edge-lengths, an O(r log n)-approximation is known from recent work of Dinitz and Krauthgamer [STOC 2011], in which several spanner results are obtained using a common approach of rounding a natural flow-based linear programming relaxation. Here we use a different (stronger) LP relaxation and improve the approximation ratio to O(log n), which is, notably, independent of the number of faults r. We further strengthen this bound in terms of the maximum degree by using the Lovasz Local Lemma. Finally, we show that most of our constructions are inherently local by designing equivalent distributed algorithms in the LOCAL model of distributed computation.