A new upper bound on the complexity of the all pairs shortest path problem
Information Processing Letters
On the exponent of the all pairs shortest path problem
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
All Pairs Shortest Paths in weighted directed graphs ? exact and almost exact algorithms
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Improved algorithm for all pairs shortest paths
Information Processing Letters
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
An O(n3loglogn/logn) time algorithm for the all-pairs shortest path problem
Information Processing Letters
Efficient algorithms for the weighted 2-center problem in a cactus graph
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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This paper achieves O(n3loglogn/logn) time for the 2-center problems on a directed graph with non-negative edge costs under the conventional RAM model where only arithmetic operations, branching operations, and random accessibility with O(logn) bits are allowed. Here n is the number of vertices. This is a slight improvement on the best known complexity of those problems, which is O(n3). We further show that when the graph is with unit edge costs, one of the 2-center problems can be solved in O(n2.575) time.