Worst-case Analysis of Set Union Algorithms
Journal of the ACM (JACM)
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Union-find with constant time deletions
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
| Hi-index | 5.23 |
The Union-Find data structure for maintaining disjoint sets is one of the best known and widespread data structures, in particular the version with constant-time Union and efficient Find. Recently, the question of how to handle deletions from the structure in an efficient manner has been taken up, first by Kaplan et al. (2002) [2] and subsequently by Alstrup et al. (2005) [1]. The latter work shows that it is possible to implement deletions in constant time, without affecting adversely the asymptotic complexity of other operations, even when this complexity is calculated as a function of the current size of the set. In this note we present a conceptual and technical simplification of the algorithm, which has the same theoretical efficiency, and is probably more attractive in practice.