Patterns and pattern-matching in trees: an analysis
Information and Control
Unification: a multidisciplinary survey
ACM Computing Surveys (CSUR)
Algebraic simplification in computer algebra: an analysis of bottom-up algorithms
Theoretical Computer Science
Proceedings of the 18th international colloquium on Automata, languages and programming
Average-case analysis of algorithms and data structures
Handbook of theoretical computer science (vol. A)
Average-case analysis of unification algorithms
STACS '91 Selected papers of the 8th annual symposium on Theoretical aspects of computer science
Randomized algorithms
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Journal of the ACM (JACM)
A unifying look at data structures
Communications of the ACM
The height of a binary search tree: the limiting distribution perspective
Theoretical Computer Science
Average-Case Analysis of Pattern-Matching in Trees under the BST Probability Model
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Combinatorial Enumeration
Singularity analysis, Hadamard products, and tree recurrences
Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Reductions in binary search trees
Theoretical Computer Science
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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.