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Fringe analysis for parallel MacroSplit insertion algorithms in 2--3 trees

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Baeza-Yates, Ricardo
Gabarró Vallès, JoaquimMés informacióMés informacióMés informació
Messeguer Peypoch, XavierMés informacióMés informacióMés informació
Document typeResearch report
Defense date1997-09
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
We extend the fringe analysis (used to study the expected behavior of balanced search trees under sequential insertions) to deal with synchronous parallel insertions on 2--3 trees. Given an insertion of k keys in a tree with n nodes, the fringe evolves following a transition matrix whose coefficients take care of the precise form of the algorithm but does not depend on k or n. The derivation of this matrix uses the binomial transform recently developed by P. Poblete, J. Munro and Th. Papadakis. Due to the complexity of the preceding exact analysis, we develop also two approximations. A first one based on a simplified parallel model, and a second one based on the sequential model. These two approximated analysis prove that the parallel insertions case does not differ significantly from the sequential case, namely on the terms O(1/n^2).
CitationBaeza-Yates, R., Gabarro, J., Messeguer, X. "Fringe analysis for parallel MacroSplit insertion algorithms in 2--3 trees". 1997. 
Is part ofLSI-97-38-R
URIhttp://hdl.handle.net/2117/96525
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