Complexity of network synchronization
Journal of the ACM (JACM)
Reconstructing the shape of a tree from observed dissimilarity data
Advances in Applied Mathematics
A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximate distance oracles for unweighted graphs in Õ (n2) time
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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
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
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
Approximate distance oracles for unweighted graphs in expected O(n2) time
ACM Transactions on Algorithms (TALG)
Analysis of Topology Aggregation techniques for QoS routing
ACM Computing Surveys (CSUR)
Dynamic algorithms for graph spanners
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A near-optimal distributed fully dynamic algorithm for maintaining sparse spanners
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
On bounded leg shortest paths problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Fast deterministic distributed algorithms for sparse spanners
Theoretical Computer Science
Approximating Shortest Paths in Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Proceedings of the forty-first annual ACM symposium on Theory of computing
Small stretch spanners in the streaming model: new algorithms and experiments
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Local computation of nearly additive spanners
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
f-sensitivity distance Oracles and routing schemes
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Fast distributed graph partition and application
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
ACM Transactions on Algorithms (TALG)
Multiplicative approximations of random walk transition probabilities
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Spectral sparsification via random spanners
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Fast deterministic distributed algorithms for sparse spanners
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
On spanners of geometric graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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
Small stretch pairwise spanners
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Let G(V, E) be an undirected weighted graph with |V| = n, and |E| = m. A t-spanner of the graph G(V, E) is a sub-graph G(V, ES) such that the distance between any pair of vertices in the spanner is at most t times the distance between the two in the given graph. A 1963 girth conjecture of Erdös implies that Ω(n1+1/k) edges are required in the worst case for any (2k - 1)-spanner, which has been proved for k = 1, 2, 3, 5. There exist polynomial time algorithms that can construct spanners with the size that matches this conjectured lower bound, and the best known algorithm takes O(mn1/k) expected running time. In this paper, we present an extremely simple linear time randomized algorithm that constructs (2k - 1)-spanner of size matching the conjectured lower bound. Our algorithm requires local information for computing a spanner, and thus can be adapted suitably to obtain efficient distributed and parallel algorithms.