A lower bound on the complexity of the union-split-find problem
SIAM Journal on Computing
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
Data structures on event graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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Predecessor searching is a fundamental data structuring problem and at the core of countless algorithms: given a totally ordered universe U with n elements, maintain a subset S@?U such that for each element x@?U its predecessor in S can be found efficiently. During the last thirty years the problem has been studied extensively and optimal algorithms in many classical models of computation are known. In 1988, Mehlhorn et al. [K. Mehlhorn, S. Naher, H. Alt, A lower bound on the complexity of the union-split-find problem, SIAM J. Comput. 17 (6) (1988) 1093-1102] showed an amortized lower bound of @W(loglogn) in the pointer machine model. We give a different proof for this bound which sheds new light on the question of how much power the adversary actually needs.