An optimal synchronizer for the hypercube
SIAM Journal on Computing
Routing with polynomial communication-space trade-off
SIAM Journal on Discrete Mathematics
Near-Linear Time Construction of Sparse Neighborhood Covers
SIAM Journal on Computing
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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
Approximate distance oracles for unweighted graphs in Õ (n2) time
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
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
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
Proximity-preserving labeling schemes
Journal of Graph Theory
Fast algorithms for constructing t-spanners and paths with stretch t
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
ACM Transactions on Algorithms (TALG)
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
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
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
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Let G=(V,E) be an undirected unweighted graph on n vertices. A subgraph H of G is called an (α,β) spanner of G if for each (u,v)∈V ×V, the u-v distance in H is at most α·δG(u,v)+β. The following is a natural relaxation of the above problem: we care for only certain distances, these are captured by the set $\mathcal{P} \subseteq V \times V$ and the problem is to construct a sparse subgraph H, called an (α,β) $\mathcal{P}$-spanner, where for every $(u,v) \in \mathcal{P}$, the u-v distance in H is at most α·δG(u,v)+β. We show how to construct a (1,2) $\mathcal{P}$-spanner of size $\tilde{O}(n\cdot|\mathcal{P}|^{1/3})$ and a (1,2) (S×V)-spanner of size $\tilde{O}(n\cdot(n|S|)^{1/4})$. A D-spanner is a $\mathcal{P}$-spanner when $\mathcal{P}$ is described implicitly via a distance threshold D as P = {(u,v): δ(u,v) ≥ D}. For a given D∈ℤ+, we show how to construct a (1,4) D-spanner of size $\tilde{O}(n^{3/2}/{D^{1/4}})$ and for D≥2, a (1,4logD) D-spanner of size $\tilde{O}(n^{3/2}/{\sqrt{D}})$.