A subquadratic algorithm for constructing approximately optimal binary search trees
Journal of Algorithms
Heuristics for optimum binary search trees and minimum weight triangulation problems
Theoretical Computer Science
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Theoretical Computer Science
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
On binary searching with non-uniform costs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Strategies for Searching with Different Access Costs
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
A new approach to construct near-optimal binary search trees using genetic algorithm
AIAP'07 Proceedings of the 25th conference on Proceedings of the 25th IASTED International Multi-Conference: artificial intelligence and applications
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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.