A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
An optimal synchronizer for the hypercube
SIAM Journal on Computing
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
Polylog-time and near-linear work approximation scheme for undirected shortest paths
Journal of the ACM (JACM)
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Compact routing with minimum stretch
Journal of Algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Introduction to 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)
New constructions of (α, β)-spanners and purely additive spanners
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
On space-stretch trade-offs: upper bounds
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Lower Bounds for Additive Spanners, Emulators, and More
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Faster Algorithms for Approximate Distance Oracles and All-Pairs Small Stretch Paths
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Sparse spanners vs. compact routing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Fully dynamic randomized algorithms for graph spanners
ACM Transactions on Algorithms (TALG)
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 consider the problem of efficiently finding an additive C-spanner of an undirected unweighted graph G, that is, a subgraph H so that for all pairs of vertices u, v, δH(u, v) ≤ δG(u, v) + C, where δ denotes shortest path distance. It is known that for every graph G, one can find an additive 6-spanner with O(n4/3) edges in O(mn2/3) time. It is unknown if there exists a constant C and an additive C-spanner with o(n4/3) edges. Moreover, for C ≤ 5 all known constructions require Ω(n3/2) edges. We give a significantly more efficient construction of an additive 6- spanner. The number of edges in our spanner is n4/3polylog n, matching what was previously known up to a polylogarithmic factor, but we greatly improve the time for construction, from O(mn2/3) to n2polylog n. Notice that mn2/3 ≤ n2 only if m ≤ n4/3, but in this case G itself is a sparse spanner. We thus provide both the fastest and the sparsest (up to logarithmic factors) known construction of a spanner with constant additive distortion. We give similar improvements in the construction time of additive spanners under the assumption that the input graph has large girth, or more generally, the input graph has few edges on short cycles.