All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Journal of Algorithms
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
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
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Ramsey partitions and proximity data structures
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
Distance Oracles for Unweighted Graphs: Breaking the Quadratic Barrier with Constant Additive Error
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Approximating Shortest Paths in Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Distance Oracles beyond the Thorup-Zwick Bound
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
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
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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Given an undirected graph G with m edges, n vertices, and non-negative edge weights, and given an integer k ≥ 1, we show that for some universal constant c, a (2k − 1)-approximate distance oracle for G of size O(kn1+1/k) can be constructed in [EQUATION] time and can answer queries in O(k) time. We also give an oracle which is faster for smaller k. Our results break the quadratic preprocessing time bound of Baswana and Kavitha for all k ≥ 6 and improve the O(kmn1/k) time bound of Thorup and Zwick except for very sparse graphs and small k. When m = [EQUATION] and k = O(1), our oracle is optimal w.r.t. both stretch, size, preprocessing time, and query time, assuming a widely believed girth conjecture by Erdős.