Worst-case Analysis of Set Union Algorithms
Journal of the ACM (JACM)
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
Data structures and algorithms for disjoint set union problems
ACM Computing Surveys (CSUR)
An Efficient Algorithm to Compute Row and Column Counts for Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
Lower bounds for the union-find and the split-find problem on pointer machines
Journal of Computer and System Sciences
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
A Discipline of Programming
Optimizing two-pass connected-component labeling algorithms
Pattern Analysis & Applications
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Determination of maximally stable extremal regions in large images
SPPRA '08 Proceedings of the Fifth IASTED International Conference on Signal Processing, Pattern Recognition and Applications
A scalable parallel union-find algorithm for distributed memory computers
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part I
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
A new scalable parallel DBSCAN algorithm using the disjoint-set data structure
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Scalable parallel OPTICS data clustering using graph algorithmic techniques
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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The disjoint-set data structure is used to maintain a collection of non-overlapping sets of elements from a finite universe. Algorithms that operate on this data structure are often referred to as Union-Find algorithms. They are used in numerous practical applications and are also available in several software libraries. This paper presents an extensive experimental study comparing the time required to execute 55 variations of Union-Find algorithms. The study includes all the classical algorithms, several recently suggested enhancements, and also different combinations and optimizations of these. Our results clearly show that a somewhat forgotten simple algorithm developed by Rem in 1976 is the fastest, in spite of the fact that its worst-case time complexity is inferior to that of the commonly accepted “best” algorithms.