Complexity of network synchronization
Journal of the ACM (JACM)
Reconstructing the shape of a tree from observed dissimilarity data
Advances in Applied Mathematics
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)
Introduction to algorithms
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
Small stretch spanners in the streaming model: new algorithms and experiments
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd 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
Computing graph spanners in small memory: fault-tolerance and streaming
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
| Hi-index | 5.24 |
We present algorithms for computing small stretch (@a,@b)-spanners in the streaming model. An (@a,@b)-spanner of a graph G 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 @b. We assume that the graph is given as a stream of edges and vertices, and that only one pass over the data is allowed. Furthermore, the number of vertices and edges are not known in advance. We denote by m the current number of scanned edges and by n the current number of discovered vertices. 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(n^1^+^1^/^k) edges and our algorithms use only O(n^1^+^1^/^k) words of memory space. In case only @Q(n) internal memory is available, the same spanners can be computed using O(n^1^+^1^/^k/B) external memory blocks, each of size B. Each edge/vertex is processed in O(1) amortized time, plus O(1/B) amortized block transfers.