On Conditional Branches in Optimal Decision Trees

The decision tree is one of the most fundamental ing abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) "less than" versus "greater than or equal to" tests in order to determine one of n outcome events. The process of finding an optimal alphabetic binary tree for a known probability distribution on outcome events usually has the underlying assumption that the cost (time) per decision is uniform and thus independent of the outcome of the decision. This assumption, however, is incorrect in the case of software to be optimized for a given microprocessor, e.g., in compiling switch statements or in fine-tuning program bottlenecks. The operation of the microprocessor generally means that the cost for the more likely decision outcome can or will be less -- often far less -than the less likely decision outcome. Here we formulate a variety of O(n3 )-time O(n2 )-space dynamic programming algorithms to sol...

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Michael B. Baer
• Keywords: Alphabetic Binary Tree, CORR 2006, Education, Fundamental Ing Abstractions, Likely Decision