neal young / Chrobak23Classification

working paper:22(2023)Given a weighted, ordered query set \(Q\) and a partition of \(Q\) into classes, we study the problem of computing a minimumcost decision tree that, given any query \(q\) in \(Q\), uses equality tests and lessthan comparisons to determine the class to which \(q\) belongs. Such a tree can be much smaller than a lookup table, and much faster and smaller than a conventional search tree. We give the first polynomialtime algorithm for the problem. The algorithm extends naturally to the setting where each query has multiple allowed classes.
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