Universidad Complutense de Madrid
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Binary search trees, recurrent properties and wave equations

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Fernández Camacho, María Inés and Sánchez Couso, José Ramón (2007) Binary search trees, recurrent properties and wave equations. Fundamenta informaticae, 81 (4). pp. 409-439. ISSN 0169-2968

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Abstract

We give a generic framework to analyze the average-case running time for computing the so-called recurrent properties for pairs of binary search trees. Recurrent properties are algorithms that operate on pairs of trees testing some characteristic on nodes by performing a preorder traversal on both trees. Analysis of recurrent properties using the probability model associated with randomly grown binary search trees leads to wave equations. We use a “normalized" integral equation as a pattern to model a specific wave equation and investigate the asymptotic behavior of its solution. This methodology is applied to some particular cases of recurrent properties like testing equality, detecting direct occurrences and clashes or pattern matching


Item Type:Article
Uncontrolled Keywords:average case analysis; generating function; binary search tree; singularity analysis; integral equation; asymptotic expansion
Subjects:Sciences > Computer science
ID Code:20587
Deposited On:22 Mar 2013 12:12
Last Modified:09 Aug 2018 08:48

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