Classification via Two-Way Comparisons

Given a weighted, ordered query set \(Q\) and a partition of \(Q\) into classes, we study the problem of computing a minimum-cost decision tree that, given any query \(q\in Q\) , uses equality tests and less-than tests to determine \(q\) 's class. Such a tree can be faster and smaller than a conventional search tree and smaller than a lookup table (both of which must identify \(q\) , not just its class). We give the first polynomial-time algorithm for the problem. The algorithm extends naturally to the setting where each query has multiple allowed classes.