On Greedy Algorithms for Decision Trees

Abstract

In the general search problem we want to identify a specific element using a set of allowed tests. The general goal is to minimize the number of tests performed, although different measures are used to capture this goal. In this work we introduce a novel greedy approach that achieves the best known approximation ratios simultaneously for many different variations of this identification problem. In addition to this flexibility, our algorithm admits much shorter and simpler analyses than previous greedy strategies. As a second contribution, we investigate the potential of greedy algorithms for the more restricted problem of identifying elements of partially ordered sets by comparison with other elements. We prove that the latter problem is as hard to approximate as the general identification problem. As a positive result, we show that a natural greedy strategy achieves an approximation ratio of 2 for tree-like posets, improving upon the previously best known 14-approximation for this problem.