All pairs lightest shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Compact roundtrip routing in directed networks (extended abstract)
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
Finding least common ancestors in directed acyclic graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computing shortest paths with comparisons and additions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Oracles for distances avoiding a link-failure
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Improved Bounds and New Trade-Offs for Dynamic All Pairs Shortest Paths
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the Difficulty of Some Shortest Path Problems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
A Space Saving Trick for Directed Dynamic Transitive Closure and Shortest Path Algorithms
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
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
Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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
The aggregation and cancellation techniques as a practical tool for faster matrix multiplication
Theoretical Computer Science - Algebraic and numerical algorithm
Improved algorithm for all pairs shortest paths
Information Processing Letters
An O(n3log logn/logn) time algorithm for the all-pairs shortest path problem
Information Processing Letters
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
On the difficulty of some shortest path problems
ACM Transactions on Algorithms (TALG)
A Multiple Pairs Shortest Path Algorithm
Transportation Science
A note of an O(n3/logn) time algorithm for all pairs shortest paths
Information Processing Letters
An O(n3loglogn/logn) time algorithm for the all-pairs shortest path problem
Information Processing Letters
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
A panoply of quantum algorithms
Quantum Information & Computation
Subquadratic algorithm for dynamic shortest distances
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Constant-time all-pairs geodesic distance query on triangle meshes
I3D '12 Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Efficient algorithms for the 2-center problems
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part II
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We present two new algorithms for solving the ALL PAIRS SHORTEST PATHS (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms.The first algorithm solves the APSP problem for weighted directed graphs in which the edge weights are integers of small absolute value in $\Ot(n^{2+\mu})$ time, where $\mu$ satisfies the equation $\omega(1,\mu,1)=1+2\mu$ and $\omega(1,\mu,1)$ is the exponent of the multiplication of an $n\times n^\mu$ matrix by an $n^\mu \times n$ matrix. The currently best available bounds on $\omega(1,\mu,1)$, obtained by Coppersmith and Winograd, and by Huang and Pan, imply that $\mu0$ is an error parameter and~$W$ is the largest edge weight in the graph, after the edge weights are scaled so that the smallest non-zero edge weight in the graph is~1. It returns estimates of all the distances in the graph with a stretch of at most $1+\eps$. Corresponding paths can also be found efficiently.