Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
An improved equivalence algorithm
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
On the expected behavior of disjoint set union algorithms
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Data structures and algorithms for disjoint set union problems
ACM Computing Surveys (CSUR)
Expected deadlock time in a multiprocessing system
Journal of the ACM (JACM)
Finding connected components on a scan line array processor
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
Reference machines require non-linear time to maintain disjoint sets
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Computing integrated costs of sequences of operations with application to dictionaries
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
Stochastic coalescence in logarithmic time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
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In this paper we study the expected running time of a variety of algorithms that perform set merging. The set merging problem (for example, see AHU [1]) is concerned with using suitable data structures to represent partition of a set S &equil; { 1,2, .... ,n} so that a sequence of instructions of the form “x &Xgr; y”, meaning “Find the subset containing x; Find the subset containing y; Merge the two subsets if they are different.” may be carried out efficiently. Several alternative data structures for solving this problem are known, and their worse-case complexity fairly well understood [3], [4], [5], [8]. In contrast, the average behavior of even the most basic of these schemes remains an open problem [6]. It is the purpose of the present paper to determine the average behavior for several of the set merging algorithms commonly known.