A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
An optimal synchronizer for the hypercube
SIAM Journal on Computing
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Efficient algorithms for constructing fault-tolerant geometric spanners
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
New Results of Fault Tolerant Geometric Spanners
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Spanners and message distribution in networks
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
Fault-Tolerant Geometric Spanners
Discrete & Computational Geometry
Journal of the ACM (JACM)
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Faster Algorithms for Approximate Distance Oracles and All-Pairs Small Stretch Paths
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Fault-tolerant spanners for general graphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
ACM Transactions on Algorithms (TALG)
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Fault-tolerant spanners: better and simpler
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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Graph spanners are sparse subgraphs that preserve the distances of the original graph, up to some small multiplicative factor or additive term (known as the stretch of the spanner). A number of algorithms are known for constructing sparse spanners with small multiplicative or additive stretch. Recently, the problem of constructing fault-tolerant multiplicative spanners for general graphs was given some algorithms. This paper addresses the analogous problem of constructing fault tolerant additive spanners for general graphs. We establish the following general result. Given an n-vertex graph G, if H1 is an ordinary additive spanner for G with additive stretch α, and H2 is a fault tolerant multiplicative spanner for G, resilient against up to f edge failures, with multiplicative stretch μ, then H=H1∪H2 is an additive fault tolerant spanner of G, resilient against up to f edge failures, with additive stretch $O(\tilde{f}(\alpha+\mu))$ where $\tilde{f}$ is the number of failures that have actually occurred $(\tilde{f}\leq f)$. This allows us to derive a poly-time algorithm ${\texttt Span}^{f-t}_{add}$ for constructing an additive fault tolerant spanner H of G, relying on the existence of algorithms for constructing fault tolerant multiplicative spanners and (ordinary) additive spanners. In particular, based on some known spanner construction algorithms, we show how to construct for any n-vertex graph G an additive fault tolerant spanner with additive stretch $O(\tilde{f})$ and size O(fn4/3).