There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
An optimal synchronizer for the hypercube
SIAM Journal on Computing
Extremal graphs with no C4,s, or C10,s
Journal of Combinatorial Theory Series B
New sparseness results on graph spanners
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Journal of Algorithms
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the red-blue set cover problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
On the Hardness of Approximation Spanners
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximating k-Spanner Problems for k
Approximating k-Spanner Problems for k < 2
The Client-Server 2-Spanner Problem and Applications to Network Design
The Client-Server 2-Spanner Problem and Applications to Network Design
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Sparse distance preservers and additive spanners
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for Edge-Dilation k-Center Problems
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Exact and Approximate Distances in Graphs - A Survey
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Approximate distance oracles for unweighted graphs in Õ (n2) time
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient algorithms for constructing (1+,ε, β)-spanners in the distributed and streaming models
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
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
Approximating k-spanner problems for k 2
Theoretical Computer Science
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
Interval routing in reliability networks
Theoretical Computer Science - Foundations of software science and computation structures
On bounded leg shortest paths problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Spanners for bounded tree-length graphs
Theoretical Computer Science
Distributed algorithms for ultrasparse spanners and linear size skeletons
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
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)
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
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
An approximation algorithm for the edge-dilation k-center problem
Operations Research Letters
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
HDLBR: A name-independent compact routing scheme for power-law networks
Computer Communications
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An (&agr;,&Bgr;)-spanner of a graph G is a subgraph H such that d_H(u,w)\le &agr\cdot d_G(u,w)+&Bgr for every pair of vertices u,w, where d_{G'}(u,w) denotes the distance between two vertices u and v in G'. It is known that every graph G has a polynomially constructible (2&kgr;-1,0)-spanner (a.k.a. multiplicative (2&kgr;-1)-spanner) of size O(n^{1+1/&kgr}) for every integer &kgr\ge 1, and a polynomially constructible (1,2)-spanner (a.k.a. additive 2-spanner) of size \tO(n^{3/2}). This paper explores hybrid spanner constructions (involving both multiplicative and additive factors) for general graphs and shows that the multiplicative factor can be made arbitrarily close to 1 while keeping the spanner size arbitrarily close to O(n), at the cost of allowing the additive term to be a sufficiently large constant. More formally, we show that for any constant &egr, &dgr 0 there exists a constant &Bgr = &Bgr(&egr, &dgr) such that for every n-vertex graph G there is an efficiently constructible (1+ &egr, &Bgr)-spanner of size O(n^{1 + &dgr}). It follows that for any constant &egr, &dgr 0 there exists a constant &Bgr(&egr, &dgr) such that for any n-vertex graph G = (V,E) there exists an efficiently constructible subgraph (V,H) with O(n^{1 +&dgr}) edges such that d_H(u,w) \le (1 + &egr) d_G(u,w) for every pair of vertices.