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Optimal binary search trees with costs depending on the access paths |
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| Authors: | Jayme L. Szwarcfiter, Gonzalo Navarro, Ricardo Baeza-Yates, Joí sa de S. Oliveira, Walter Cunto,Ní vio Ziviani, |
| Affiliation: | a Universidade Federal do Rio de Janeiro, Instituto de Matemática, NCE and COPPE, Caixa Postal 2324, 20001-970, Rio de Janeiro, RJ, Brazil b Departamento de Ciencias de la Computación, Universidad de Chile, Blanco Encalada 2120, Santiago, Chile c Universidade Federal do Rio de Janeiro, COPPE, Caixa Postal 68511, 21945-970, Rio de Janeiro, RJ, Brazil d Depto. de Computación, Universidad Simón Bolívar, Apartado 89000, Caracas, Venezuela e Universidade Federal de Minas Gerais, Departamento de Ciência da Computação, 31270-010, Belo Horizonte, MG, Brazil |
| Abstract: | We describe algorithms for constructing optimal binary search trees, in which the access cost of a key depends on the k preceding keys which were reached in the path to it. This problem has applications to searching on secondary memory and robotics. Two kinds of optimal trees are considered, namely optimal worst case trees and weighted average case trees. The time and space complexities of both algorithms are O(nk+2) and O(nk+1), respectively. The algorithms are based on a convenient decomposition and characterizations of sequences of keys which are paths of special kinds in binary search trees. Finally, using generating functions, we present an exact analysis of the number of steps performed by the algorithms. |
| Keywords: | Algorithms Optimal binary search trees Generating functions |
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