Computational Complexity of Three Central Problems in Itemset Mining

TL;DR

This paper investigates the computational complexity of three key itemset mining problems, establishing NP-hardness and coNP-hardness results for various tasks in knowledge discovery.

Contribution

It provides the first formal complexity proofs for these fundamental itemset mining problems, clarifying their computational limits.

Findings

Mining confident rules with a specific item in the head is NP-hard.

Mining high utility itemsets is NP-hard.

Mining maximal or closed itemsets with constraints is coNP-hard.

Abstract

Itemset mining is one of the most studied tasks in knowledge discovery. In this paper we analyze the computational complexity of three central itemset mining problems. We prove that mining confident rules with a given item in the head is NP-hard. We prove that mining high utility itemsets is NP-hard. We finally prove that mining maximal or closed itemsets is coNP-hard as soon as the users can specify constraints on the kind of itemsets they are interested in.