Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Introduction to algorithms
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Journal of Algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Exact and Approximate Distances in Graphs - A Survey
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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)
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
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
Approximate distance oracles for unweighted graphs in expected O(n2) time
ACM Transactions on Algorithms (TALG)
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
Efficient algorithms on sets of permutations, dominance, and real-weighted APSP
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
All-pairs nearly 2-approximate shortest-paths in O(n2 polylog n) time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
ESA'11 Proceedings of the 19th European conference on Algorithms
Approximate distance oracles with improved preprocessing time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fully dynamic randomized algorithms for graph spanners
ACM Transactions on Algorithms (TALG)
Fast approximation algorithms for the diameter and radius of sparse graphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Small stretch pairwise spanners
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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Let $G=(V,E)$ be a weighted undirected graph having nonnegative edge weights. An estimate $\hat{\delta}(u,v)$ of the actual distance $\delta(u,v)$ between $u,v\in V$ is said to be of stretch $t$ if and only if $\delta(u,v)\leq\hat{\delta}(u,v)\leq t\cdot\delta(u,v)$. Computing all-pairs small stretch distances efficiently (both in terms of time and space) is a well-studied problem in graph algorithms. We present a simple, novel, and generic scheme for all-pairs approximate shortest paths. Using this scheme and some new ideas and tools, we design faster algorithms for all-pairs $t$-stretch distances for a whole range of stretch $t$, and we also answer an open question posed by Thorup and Zwick in their seminal paper [J. ACM, 52 (2005), pp. 1-24].