Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
The pairing heap: a new form of self-adjusting heap
Algorithmica
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
A data structure for dynamic trees
Journal of Computer and System Sciences
The cell probe complexity of dynamic data structures
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
An introduction to parallel algorithms
An introduction to parallel algorithms
Verification and sensitivity analysis of minimum spanning trees in linear time
SIAM Journal on Computing
Surpassing the information theoretic bound with fusion trees
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
The minimum spanning tree problem on a planar graph
Discrete Applied Mathematics
Randomized algorithms
Ambivalent Data Structures for Dynamic 2-Edge-Connectivity and k Smallest Spanning Trees
SIAM Journal on Computing
Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
Linear-time pointer-machine algorithms for least common ancestors, MST verification, and dominators
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Fusion trees can be implemented with AC0 instructions only
Theoretical Computer Science
Backwards analysis of the Karger-Klein-Tarjan algorithm for minimum spanning trees
Information Processing Letters
On an algorithm of Zemlyachenko for subtree isomorphism
Information Processing Letters
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Randomized fully dynamic graph algorithms with polylogarithmic time per operation
Journal of the ACM (JACM)
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Applications of Path Compression on Balanced Trees
Journal of the ACM (JACM)
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Floats, integers, and single source shortest paths
Journal of Algorithms
A new approximation algorithm for the Steiner tree problem with performance ratio 5/3
Journal of Algorithms
The soft heap: an approximate priority queue with optimal error rate
Journal of the ACM (JACM)
A minimum spanning tree algorithm with inverse-Ackermann type complexity
Journal of the ACM (JACM)
A data structure for manipulating priority queues
Communications of the ACM
Communications of the ACM
Concurrent threads and optimal parallel minimum spanning trees algorithm
Journal of the ACM (JACM)
An optimal minimum spanning tree algorithm
Journal of the ACM (JACM)
Deterministic sorting in O(nlog log n) time and linear space
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Journal of Algorithms
Efficient minimum spanning tree construction without Delaunay triangulation
Information Processing Letters
Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Nearest common ancestors: a survey and a new distributed algorithm
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Purely Functional Data Structures
Purely Functional Data Structures
On AC0 implementations of fusion trees and atomic heaps
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Sublinear-time approximation of Euclidean minimum spanning tree
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Integer Sorting in 0(n sqrt (log log n)) Expected Time and Linear Space
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Maintaining Minimum Spanning Trees in Dynamic Graphs
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Improved Shortest Paths on the Word RAM
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Sorting and Searching on the Word RAM
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Minimum Spanning Trees for Minor-Closed Graph Classes in Parallel
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Efficient Initial Approximation and Fast Converging Methods for Division and Square Root
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
A Faster Deterministic Algorithm for Minimum Spanning Trees
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Time-bounded random access machines
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
HAKMEM
Finding Minimum Spanning Trees in O(m alpha(m,n)) Time
Finding Minimum Spanning Trees in O(m alpha(m,n)) Time
Estimating the weight of metric minimum spanning trees in sublinear-time
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - Special issue: STOC 2003
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Approximating the Minimum Spanning Tree Weight in Sublinear Time
SIAM Journal on Computing
Towards a Final Analysis of Pairing Heaps
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
An Õ(mn) Gomory-Hu tree construction algorithm for unweighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Random sampling in matroids, with applications to graph connectivity and minimum spanning trees
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
On the History of the Minimum Spanning Tree Problem
IEEE Annals of the History of Computing
Journal of Computer and System Sciences
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Linear-time ranking of permutations
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Fast and memory-efficient minimum spanning tree on the GPU
International Journal of Computational Science and Engineering
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This article surveys the many facets of the Minimum Spanning Tree problem. We follow the history of the problem since the first polynomial-time solution by Bor@?uvka to the modern algorithms by Chazelle, Pettie and Ramachandran. We study the differences in time complexity dependent on the model of computation chosen and on the availability of random bits. We also briefly touch the dynamic maintenance of the MST and other related problems.