Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Faster algorithms for the shortest path problem
Journal of the ACM (JACM)
Finding the hidden path: time bounds for all-pairs shortest paths
SIAM Journal on Computing
Shortest paths algorithms: theory and experimental evaluation
Mathematical Programming: Series A and B
Algorithm 360: shortest-path forest with topological ordering [H]
Communications of the ACM
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Sharing information in all pairs shortest path algorithms
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Sharing information for the all pairs shortest path problem
Theoretical Computer Science
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In this paper we deal with a directed graph G = (V, E) with non-negative integer edge costs where the edge costs are bounded by c and |V| = n and m = |E|. We show the all pairs shortest path (APSP) problem can be solved in O(mn + n2 log(c/n))) time with the data structure of cascading bucket system. The idea for speed-up is to share a single priority queue among n single source shortest path (SSSP) problems that are solved for APSP. We use the traditional computational model such that comparison-addition operations on distance data and random access with O(log n) bits can be done in O(1) time. Also the graph is not separated, meaning m ≥ n. Our complexity is best for a relatively large bound on edge cost, c, such that c = o(n log n).