Restrictions of minimum spanner problems
Information and Computation
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
External memory algorithms and data structures: dealing with massive data
ACM Computing Surveys (CSUR)
New constructions of (α, β)-spanners and purely additive spanners
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Graph distances in the streaming model: the value of space
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
Dynamic algorithms for graph spanners
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Fully dynamic algorithm for graph spanners with poly-logarithmic update time
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Streaming algorithm for graph spanners---single pass and constant processing time per edge
Information Processing Letters
Fault-tolerant spanners for general graphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Graph Spanners in the Streaming Model: An Experimental Study
Algorithmica - Special Issue: European Symposium on Algorithms 2007, Guest Editors: Larse Arge and Emo Welzl
Small stretch (α,β)-spanners in the streaming model
Theoretical Computer Science
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Let G be an undirected graph with m edges and n vertices. A spanner of G is a subgraph which preserves approximate distances between all pairs of vertices. An f-vertex fault-tolerant spanner is a subgraph which preserves approximate distances, under the failure of any set of at most f vertices. The contribution of this paper is twofold: we present algorithms for computing fault-tolerant spanners, and propose streaming algorithms for computing spanners in very small internal memory. In particular, we give algorithms for computing f-vertex faulttolerant (3,2)- and (2,1)-spanners of G with the following bounds: our (3,2)-spanner contains O(f4/3n4/3) edges and can be computed in time Õ (f2m), while our (2,1)-spanner contains O(fn3/2) edges and can be computed in time Õ (fm). Both algorithms improve significantly on previously known bounds. Assume that the graph G is presented as an input stream of edges, which may appear in any arbitrary order, and that we do not know in advance m and n. We show how to compute efficiently (3,2)- and (2,1)- spanners of G, using only very small internal memory and a slow access external memory device. Our spanners have asymptotically optimal size and the I/O complexity of our algorithms for computing such spanners is optimal up to a polylogarithmic factor. Our f-vertex fault-tolerant (3,2)- and (2,1)-spanners can also be computed efficiently in the same computational model described above.