Alphabetic coding with exponential costs

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Alphabetic coding with exponential costs
An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing n i=1 w(i)l(i), this variant involves minimizing loga n i=1 w(i)al(i) for a given a ∈ (0, 1). This note introduces a dynamic programming algorithm that finds the optimal solution in polynomial time and space, and shows that methods traditionally used to improve the speed of optimizations in related problems, such as the Hu-Tucker procedure, fail for this problem. This note thus also introduces two approximation algorithms which can find a suboptimal solution in linear time (for one) or O(n log n) time (for the other), with associated coding redundancy bounds. Key words: Approximation algorithms; dynamic programming; information retrieval; R´enyi entropy; tree searching
Michael B. Baer
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where IPL
Authors Michael B. Baer
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