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 path algorithms for nearly acyclic directed graphs
Theoretical Computer Science - Special issue: graph theoretic concepts in computer science
A data structure for manipulating priority queues
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
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We show two improvements on time complexities of the all pairs shortest path (APSP) problem for directed graphs that satisfy certain properties. The idea for speed-up is information sharing by n single source shortest path (SSSP) problems that are solved for APSP. We consider two parameters, in addition to the numbers of vertices, n, and edges, m. First we improve the time complexity of O(mn + n2 √log c) to O(mn + nc) for the APSP problem with the integer edge costs bounded by c. When c ≤ O(n√log n), this complexity is better than the previous one. Next we consider a nearly acyclic graph. 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 improve the existing time complexity of O(mn + r3) for the all pairs shortest path problem to O(mn + rn log n) by some kind of information sharing. This complexity is better than the previous one for all values of r under a reasonable assumption of m ≥ n.