A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
Introduction to algorithms
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Randomized 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)
An On-Line Edge-Deletion Problem
Journal of the ACM (JACM)
Compact routing with minimum stretch
Journal of Algorithms
Sparse distance preservers and additive spanners
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Compact roundtrip routing in directed networks
Journal of Algorithms
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
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
A new approach to dynamic all pairs shortest paths
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Sparse source-wise and pair-wise distance preservers
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Metric Embeddings with Relaxed Guarantees
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Fast distributed algorithms for (weakly) connected dominating sets and linear-size skeletons
Journal of Computer and System Sciences
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
A near-optimal distributed fully dynamic algorithm for maintaining sparse spanners
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Streaming algorithm for graph spanners---single pass and constant processing time per edge
Information Processing Letters
Improved Dynamic Reachability Algorithms for Directed Graphs
SIAM Journal on Computing
Roundtrip spanners and roundtrip routing in directed graphs
ACM Transactions on Algorithms (TALG)
On the locality of distributed sparse spanner construction
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
SIAM Journal on Computing
Graph Distances in the Data-Stream Model
SIAM Journal on Computing
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Additive spanners in nearly quadratic time
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
ACM Transactions on Algorithms (TALG)
Faster Algorithms for All-pairs Approximate Shortest Paths in Undirected Graphs
SIAM Journal on Computing
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
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Spanner of an undirected graph G = (V,E) is a subgraph that is sparse and yet preserves all-pairs distances approximately. More formally, a spanner with stretch t ∈ ℕ 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. Though G is trivially a t-spanner of itself, the research as well as applications of spanners invariably deal with a t-spanner that has as small number of edges as possible. We present fully dynamic algorithms for maintaining spanners in centralized as well as synchronized distributed environments. These algorithms are designed for undirected unweighted graphs and use randomization in a crucial manner. Our algorithms significantly improve the existing fully dynamic algorithms for graph spanners. The expected size (number of edges) of a t-spanner maintained at each stage by our algorithms matches, up to a polylogarithmic factor, the worst case optimal size of a t-spanner. The expected amortized time (or messages communicated in distributed environment) to process a single insertion/deletion of an edge by our algorithms is close to optimal.