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
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Journal of Algorithms
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Communication-time trade-offs in network synchronization
Proceedings of the fourth annual ACM symposium on Principles of distributed computing
Polylog-time and near-linear work approximation scheme for undirected shortest paths
Journal of the ACM (JACM)
Compact routing with minimum stretch
Journal of Algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Strong Inapproximability of the Basic k-Spanner Problem
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Compact roundtrip routing in directed networks
Journal of Algorithms
Journal of the ACM (JACM)
Approximating k-spanner problems for k 2
Theoretical Computer Science
Approximate distance oracles for unweighted graphs in expected O(n2) time
ACM Transactions on Algorithms (TALG)
The Hardness of Approximating Spanner Problems
Theory of Computing Systems
Roundtrip spanners and roundtrip routing in directed graphs
ACM Transactions on Algorithms (TALG)
Improved approximating algorithms for Directed Steiner Forest
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Graph Distances in the Data-Stream Model
SIAM Journal on Computing
Lower bounds for local monotonicity reconstruction from transitive-closure spanners
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Transitive-closure spanners: a survey
Property testing
Directed spanners via flow-based linear programs
Proceedings of the forty-third annual ACM symposium on Theory of computing
Label cover instances with large girth and the hardness of approximating basic k-spanner
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Approximation algorithms for spanner problems and Directed Steiner Forest
Information and Computation
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We give an O(√n log n)-approximation algorithm for the problem of finding the sparsest spanner of a given directed graph G on n vertices. A spanner of a graph is a sparse subgraph that approximately preserves distances in the original graph. More precisely, given a graph G = (V,E) with nonnegative edge lengths d : E → R≥0 and a stretch k ≥ 1, a subgraph H = (V,EH) is a k-spanner of G if for every edge (u, v) ∈ E, the graph H contains a path from u to v of length at most k ċ d(u, v). The previous best approximation ratio was Õ(n2/3), due to Dinitz and Krauthgamer (STOC '11). We also present an improved algorithm for the important special case of directed 3-spanners with unit edge lengths. The approximation ratio of our algorithm is Õ(n1/3) which almost matches the lower bound shown by Dinitz and Krauthgamer for the integrality gap of a natural linear programming relaxation. The best previously known algorithms for this problem, due to Berman, Raskhodnikova and Ruan (FSTTCS '10) and Dinitz and Krauthgamer, had approximation ratio Õ(√n).