Search in an ordered array having variable probe cost
SIAM Journal on Computing
A fast algorithm for optimal length-limited Huffman codes
Journal of the ACM (JACM)
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Codes: Unequal Probabilities, Unequal Letter Cost
Journal of the ACM (JACM)
The Art of Computer Programming Volumes 1-3 Boxed Set
The Art of Computer Programming Volumes 1-3 Boxed Set
Theory of Information and Coding
Theory of Information and Coding
A dynamic programming algorithm for constructing optimal prefix-free codes with unequal letter costs
IEEE Transactions on Information Theory
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We investigate code trees and search trees with cost functions that increase exponentially with the depth in the tree. While corresponding coding theorems have been considered in connection with Renyi's entropy since 1965, the algorithmic aspects of these constructions have not been analyzed before. We propose a generalized Huffman algorithm for the construction of optimal codes in this model and treat related questions for search trees giving bounds on the costs of optimal trees. The algorithm for search tree construction is based on a new form of dynamic programming with the quadrangle inequality. We also consider random trees. Due to the exponential cost function, optimally balanced trees turn out to have significantly lower average costs than random trees, unlike in the standard cost model.