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Lower bounds for UnionSplitFind related problems on random access machines
, 1994
"... We prove \Omega\Gamma p log log n) lower bounds on the random access machine complexity of several dynamic, partially dynamic and static data structure problems, including the unionsplitfind problem, dynamic prefix problems and onedimensional range query problems. The proof techniques include a ..."
Abstract

Cited by 49 (3 self)
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We prove \Omega\Gamma p log log n) lower bounds on the random access machine complexity of several dynamic, partially dynamic and static data structure problems, including the unionsplitfind problem, dynamic prefix problems and onedimensional range query problems. The proof techniques include a general technique using perfect hashing for reducing static data structure problems (with a restriction of the size of the structure) into partially dynamic data structure problems (with no such restriction), thus providing a way to transfer lower bounds. We use a generalization of a method due to Ajtai for proving the lower bounds on the static problems, but describe the proof in terms of communication complexity, revealing a striking similarity to the proof used by Karchmer and Wigderson for proving lower bounds on the monotone circuit depth of connectivity. 1 Introduction and summary of results In this paper we give lower bounds for the complexity of implementing several dynamic and sta...
Backtracking
"... Contents 1 Introduction 3 2 Models of computation 6 3 The Set Union Problem 9 4 The WorstCase Time Complexity of a Single Operation 15 5 The Set Union Problem with Deunions 18 6 Split and the Set Union Problem on Intervals 22 7 The Set Union Problem with Unlimited Backtracking 26 1 Introduction A ..."
Abstract
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Contents 1 Introduction 3 2 Models of computation 6 3 The Set Union Problem 9 4 The WorstCase Time Complexity of a Single Operation 15 5 The Set Union Problem with Deunions 18 6 Split and the Set Union Problem on Intervals 22 7 The Set Union Problem with Unlimited Backtracking 26 1 Introduction An equivalence relation on a finite set S is a binary relation that is reflexive symmetric and transitive. That is, for s; t and u in S, we have that sRs, if sRt then tRs, and if sRt and tRu then sRu. Set S is partitioned by R into equivalence classes where each class cointains all and only the elements that obey R pairwise. Many computational problems involve representing, modifying and tracking the evolution of equivalenc