1 research outputs found
On Conditional Branches in Optimal Search Trees
Algorithms for efficiently finding optimal alphabetic decision trees -- such
as the Hu-Tucker algorithm -- 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. Such software generally has one
cost for the more likely decision outcome and a greater cost -- often far
greater -- for the less likely decision outcome. This problem and
generalizations thereof are thus applicable to hard coding static decision tree
instances in software, e.g., for optimizing program bottlenecks or for
compiling switch statements. An O(n^3)-time O(n^2)-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. Solutions to this
formulation are often faster in practice than ``optimal'' decision trees as
formulated in the literature. Different search paradigms can sometimes yield
even better performance.Comment: 8 pages, 5 figures (with 10 illustrations total), 1 table;
reformatted with some additional note