Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
A new upper bound on the complexity of the all pairs shortest path problem
Information Processing Letters
Finding the hidden path: time bounds for all-pairs shortest paths
SIAM Journal on Computing
An incremental algorithm for a generalization of the shortest-path problem
Journal of Algorithms
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
Introduction to Algorithms
A Faster All-Pairs Shortest Path Algorithm for Real-Weighted Sparse Graphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
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
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Sensitivity analysis of minimum spanning trees in sub-inverse-ackermann time
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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We present an all-pairs shortest path algorithm for arbitrary graphs that performs O(mn log 驴) comparison and addition operations, where m and n are the number of edges and vertices, resp., and 驴 = 驴 (m, n) is Tarjan's inverse-Ackermann function. Our alorithm e1iminates the sorting bottleneck inherent in approaches based on Dijkstra's alogrithm, and for graphs with O(n) edges Our algorithm is within a tiny O(log 驴) factor of optimal. The algorithm can be implemented to run in polynomial time (though it is not a pleasing polynomial). We leave open the problem of providing an efficient implementation.