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Reductions in binary search trees

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Sánchez Couso, José Ramón and Fernández Camacho, María Inés (2006) Reductions in binary search trees. Theoretical Computer Science, 355 (3). pp. 327-353. ISSN 0304-3975

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Official URL: http://www.sciencedirect.com/science/article/pii/S0304397506000247


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Abstract

We analyze two bottom-up reduction algorithms over binary trees that represent replaceable data within a certain system, assuming the binary search tree (BST) probabilistic model. These reductions are based on idempotent and nilpotent operators, respectively. In both cases, the average size of the reduced tree, as well as the cost to obtain it, is asymptotically linear with respect to the size of the original tree. Additionally, the limiting distributions of the size of the trees obtained by means of these reductions satisfy a central limit law of Gaussian type.


Item Type:Article
Uncontrolled Keywords:Bottom-up algorithm; Generating function; Analytic convergence; Singularity analysis; Complex asymptotics; Differential equation
Subjects:Sciences > Computer science
ID Code:20607
Deposited On:01 Apr 2013 11:07
Last Modified:06 Sep 2018 16:14

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