A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
Adapting to asynchronous dynamic networks (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Routing with polynomial communication-space trade-off
SIAM Journal on Discrete Mathematics
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
Near-Linear Time Construction of Sparse Neighborhood Covers
SIAM Journal on Computing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
(1 + &egr;&Bgr;)-spanner constructions for general graphs
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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
Roundtrip spanners and roundtrip routing in directed graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Lectures on Discrete Geometry
Sparse distance preservers and additive spanners
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
All pairs almost shortest paths
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
An Approximation Algorithm for Minimum-Cost Network Design
An Approximation Algorithm for Minimum-Cost Network Design
New constructions of (α, β)-spanners and purely additive spanners
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Proximity-preserving labeling schemes
Journal of Graph Theory
A simple linear time algorithm for computing a (2k - 1)-spanner of o(n1+1/k) size in weighted graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
On the locality of distributed sparse spanner construction
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
An improved construction of progression-free sets
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Fully dynamic randomized algorithms for graph spanners
ACM Transactions on Algorithms (TALG)
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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We introduce and study the notions of pair-wise and source-wise preservers.Given an undirected N-vertex graph G = (V, E) and a subset P of pairs of vertices, let G' = (V, H), H ⊆ E, be called a pair-wise preserver of G with respect to P if for every pair {u, w} ∈ P, distG' (u, w) = distG (u, w). For a set S ⊆ V of sources, a pair-wise preserver of G with respect to the set of all pairs P = (S/2) of sources is called a source-wise preserver of G with respect to S.We prove that for every undirected possibly weighted N-vertex graph G and every subset P of P = O(N1/2) pairs of vertices of G, there exists a linear-size pair-wise preserver of G with respect to P. Consequently, for every subset S ⊆ V of S = O(N1/4) sources, there exists a linear-size source-wise preserver of G with respect to S. On the negative side we show that neither of the two exponents (1/2 and 1/4) can be improved even when the attention is restricted to unweighted graphs.Our lower bounds involve constructions of dense convexly independent sets of vectors with small Euclidean norms. We believe that the link between the areas of Discrete Geometry and spanners that we establish is of independent interest, and might be useful in the study of other problems in the area of low-distortion embeddings.