Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
Computing shortest paths with comparisons and additions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Shortest Paths on the Word RAM
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Experimental Evaluation of a New Shortest Path Algorithm
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Exact and Approximate Distances in Graphs - A Survey
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
A scaling algorithm for weighted matching on general graphs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
On the Comparison-Addition Complexity of All-Pairs Shortest Paths
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Improved algorithm for all pairs shortest paths
Information Processing Letters
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
An O(n3 (loglogn/logn)5/4) time algorithm for all pairs shortest paths
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A note of an O(n3/logn) time algorithm for all pairs shortest paths
Information Processing Letters
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Discrete sensor placement problems in distribution networks
Mathematical and Computer Modelling: An International Journal
An O(n3 log log n/ log2 n) time algorithm for all pairs shortest paths
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Approximating the diameter of planar graphs in near linear time
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We present a faster all-pairs shortest paths algorithm for arbitrary real-weighted directed graphs. The algorithm works in the fundamental comparison-addition model and runs in O(mn+n2 log log n) time, where m and n are the number of edges & vertices, respectively. This is strictly faster than Johnson's algorithm (for arbitrary edge-weights) and Dijkstra's algorithm (for positive edge-weights) when m = o(n log n) and matches the running time of Hagerup's APSP algorithm, which assumes integer edge-weights and a more powerful model of computation.