A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
Introduction to algorithms
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
Randomized fully dynamic graph algorithms with polylogarithmic time per operation
Journal of the ACM (JACM)
Journal of Algorithms
Dynamic Approximate All-Pairs Shortest Paths in Undirected Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Fully dynamic geometric spanners
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
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
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Small stretch spanners on dynamic graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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
Distributed algorithms for ultrasparse spanners and linear size skeletons
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Fault-tolerant spanners for general graphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Computing graph spanners in small memory: fault-tolerance and streaming
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
ACM Transactions on Algorithms (TALG)
Fault Tolerant Spanners for General Graphs
SIAM Journal on Computing
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Spanner of an undirected graph G = (V, E) is a sub graph which is sparse and yet preserves all-pairs distances approximately. More precisely, a spanner with stretch t ∈ IN is a subgraph (V, ES), ES ⊆ E such that the distance between any two vertices in the subgraph is at most t times their distance in G. We present two fully dynamic algorithms for maintaining a sparse t-spanner of an unweighted graph. Our first algorithm achieves expected O(7 t/4) time per update independent of the size of the graph. This algorithm is particularly of interest for maintaining small stretch spanners. Our second algorithm achieves expected O(polylog |V|) time per update irrespective of the stretch.