A generalization of the model of permutations for binary search trees
The classical model of permutations, that allows the study of consecutive insertions in BST, fails when it considers intermixed deletions and insertions (Knott paradox). Our model solves this paradox by considering the inserted and deleted keys as Jonassen & Knuth proposed in [Jo,Knu 78], and al...
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 1991 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/330452 |
| Acceso en línea: | https://hdl.handle.net/2117/330452 |
| Access Level: | acceso abierto |
| Palabra clave: | Trees (Graph theory) Arbres (Teoria de grafs) Àrees temàtiques de la UPC::Informàtica |
| Sumario: | The classical model of permutations, that allows the study of consecutive insertions in BST, fails when it considers intermixed deletions and insertions (Knott paradox). Our model solves this paradox by considering the inserted and deleted keys as Jonassen & Knuth proposed in [Jo,Knu 78], and allows the development of the invariant theory of functions applied to algorithms, following the Knuth approach as in [Knu 77]. The model also explains the pattern defined by the first random insertions followed by random deletion, by applying the invariant properties of algorithms without computing combinatorial expressions. The model suggests a new line of research to face the general problem of intermixed randon insertions and deletions. |
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