Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
An optimal algorithm with unknown time complexity for convex matrix searching
Information Processing Letters
Verification and sensitivity analysis of minimum spanning trees in linear time
SIAM Journal on Computing
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
On the parallel time complexity of undirected connectivity and minimum spanning trees
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A Randomized Time-Work Optimal Parallel Algorithm for Finding a Minimum Spanning Forest
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Car-Pooling as a Data Structuring Device: The Soft Heap
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
A Faster Deterministic Algorithm for Minimum Spanning Trees
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
An Optimal Minimum Spanning Tree Algorithm
An Optimal Minimum Spanning Tree Algorithm
Finding Minimum Spanning Trees in O(m alpha(m,n)) Time
Finding Minimum Spanning Trees in O(m alpha(m,n)) Time
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
On the History of the Minimum Spanning Tree Problem
IEEE Annals of the History of Computing
Approximating the Minimum Spanning Tree Weight in Sublinear Time
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Experimental Evaluation of a New Shortest Path Algorithm
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Improved algorithms for replacement paths problems in restricted graphs
Operations Research Letters
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We establish that the algorithmic complexity of the minimum spanning tree problem is equal to its decision-tree complexity. Specifically, we present a deterministic algorithm to find a minimum spanning forest of a graph with n vertices and m edges that runs in time O(Τ*(m, n)) where Τ* is the minimum number of edge-weight comparisons needed to determine the solution. the algorithm is quite simple and can be implemented on a pointer machine. Although our time bound is optimal, the exact function describing it is not known at present. the current best bounds known for Τ* are Τ*(m, n) = Ω(m) and Τ*(m, n) = O(m ċ α(m, n)), where α is a certain natural inverse of Ackermann's function. Even under the assumption that Τ* is super-linear, we show that if the input graph is selected from Gn,m, our algorithm runs in linear time w.h.p., regardless of n, m, or the permutation of edge weights. the analysis uses a new martingale for Gn,m similar to the edge-exposure martingale for Gn,p.