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
Shortest path algorithms for nearly acyclic directed graphs
Theoretical Computer Science - Special issue: graph theoretic concepts in computer science
Algorithm 360: shortest-path forest with topological ordering [H]
Communications of the ACM
Improved shortest path algorithms for nearly acyclic graphs
Theoretical Computer Science
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
All-pairs shortest paths for unweighted undirected graphs in o(mn) time
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Solving shortest paths efficiently on nearly acyclic directed graphs
Theoretical Computer Science
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Sharing information in all pairs shortest path algorithms
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Efficient algorithms for the all pairs shortest path problem with limited edge costs
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
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We improve the time complexity of the all pairs shortest path (APSP) problem for special classes of directed graphs. One is a nearly acyclic directed graph and the other is a directed graph with limited edge costs. The common idea for speed-up is information sharing by n single source shortest path (SSSP) problems that are solved for APSP. We measure the degree of acyclicity by the size, r, of a given set of feedback vertices. If r is small, the given graph can be considered to be nearly acyclic. We consider this parameter, r, in addition to the traditional parameters of the number of vertices, n, and that of edges, m. In the first part we improve the existing time complexity of O(mn+r^3) for the all pairs shortest path problem to O(mn+rnlogn). This complexity is equal to or better than the previous one for all values of r under a reasonable assumption of m=n. In the second part, we deal with a directed graph with non-negative integer edge costs bounded by c. We show the all pairs shortest path (APSP) problem can be solved in O(mn+n^2log(c/n)) time with the data structure of cascading bucket system. We use the traditional computational model such that comparison-addition operations on distance data and random access with O(logn) bits can be done in O(1) time. Also the graph is not separated, meaning m=n-1.