Branching processes in the analysis of the heights of trees
Acta Informatica
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
An all pairs shortest path algorithm with expected time O(n2logn)
SIAM Journal on Computing
The expected length of a shortest path
Information Processing Letters
Finding the hidden path: time bounds for all-pairs shortest paths
SIAM Journal on Computing
Algorithmic theory of random graphs
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
On the all-pairs shortest-path algorithm of Moffat and Takaoka
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Average-case complexity of shortest-paths problems in the vertex-potential model
Random Structures & Algorithms
Algorithm 360: shortest-path forest with topological ordering [H]
Communications of the ACM
One, Two and Three Times log n/n for Paths in a Complete Graph with Random Weights
Combinatorics, Probability and Computing
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Average-case complexity of single-source shortest-paths algorithms: lower and upper bounds
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
A new approach to dynamic all pairs shortest paths
Journal of the ACM (JACM)
Worst-case update times for fully-dynamic all-pairs shortest paths
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Experimental analysis of dynamic all pairs shortest path algorithms
ACM Transactions on Algorithms (TALG)
Does path cleaning help in dynamic all-pairs shortest paths?
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A Practical Shortest Path Algorithm with Linear Expected Time
SIAM Journal on Computing
Average Update Times for Fully-Dynamic All-Pairs Shortest Paths
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
The longest minimum-weight path in a complete graph
Combinatorics, Probability and Computing
| Hi-index | 0.00 |
We present an all-pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from [0,1] is O(n2), in expectation and with high probability. This resolves a long-standing open problem. The algorithm is a variant of the dynamic all-pairs shortest paths algorithm of Demetrescu and Italiano [2006]. The analysis relies on a proof that the number of locally shortest paths in such randomly weighted graphs is O(n2), in expectation and with high probability. We also present a dynamic version of the algorithm that recomputes all shortest paths after a random edge update in O(log2n) expected time.