Complexity of network synchronization
Journal of the ACM (JACM)
There are planar graphs almost as good as the complete graph
Journal of Computer and System Sciences
An optimal synchronizer for the hypercube
SIAM Journal on Computing
Delaunay graphs are almost as good as complete graphs
Discrete & Computational Geometry
On sparse spanners of weighted graphs
Discrete & Computational Geometry
NP-completeness of minimum spanner problems
Discrete Applied Mathematics
Degree-constrained pyramid spanners
Journal of Parallel and Distributed Computing
External memory algorithms and data structures: dealing with massive data
ACM Computing Surveys (CSUR)
Which Triangulations Approximate the Complete Graph?
Proceedings of the International Symposium on Optimal Algorithms
On the Streaming Model Augmented with a Sorting Primitive
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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
Dynamic algorithms for graph spanners
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A simple linear time algorithm for computing a (2k - 1)-spanner of o(n1+1/k) size in weighted graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Streaming algorithm for graph spanners---single pass and constant processing time per edge
Information Processing Letters
Small stretch (α,β)-spanners in the streaming model
Theoretical Computer Science
Computing strongly connected components in the streaming model
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
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We present deterministic algorithms for computing small stretch spanners in the streaming model. An (α,β)-spanner of a graph G with n vertices is a subgraph S ⊆ G such that for each pair of vertices the distance in S is at most a times the distance in G plus β. We assume that the graph is given as a stream of edges in arbitrary order, that the number of vertices and the number of edges are not known in advance and that only one pass over the data is allowed. In this model, we show how to compute a (k, k-1)-spanner of an unweighted undirected graph, for k = 2, 3, in O(1) amortized processing time per edge/vertex. The computed (k, k - 1)-spanners have O(n1+1/k) edges and our algorithms use only O(n1+1/k) words of memory space. In case only Θ(n) internal memory is available, our algorithms can be adapted to store some of the data structures in external memory. We complement our theoretical analysis with an experimental study that suggests that our approach can be of practical value.