On Conditional Branches in Search Trees

Algorithms for efficiently finding optimal alphabetic decision trees for known probability distributions are well established and commonly used. However, such algorithms generally assume that the cost per decision is uniform and thus independent of the outcome of the decision. The few algorithms without this assumption instead use one cost if the decision outcome is “less than” and another cost otherwise. In practice, neither assumption is accurate for software optimized for today’s microprocessors, which generally have one cost for the more likely decision outcome and a greater cost — often far greater — for the less likely decision outcome. We investigate this problem and generalizations thereof with an emphasis on hard coding static decision tree instances. An O(n)time O(n)-space dynamic programming algorithm can solve this optimal binary decision tree problem, and this approach has many generalizations that optimize for the behavior of processors with predictive branch capabilities, both static and dynamic. Different search paradigms are also considered.