# Computational Complexity of Queries Based on Itemsets

## TL;DR

This paper explores the computational difficulty of determining exact frequency bounds of itemset conjunctions, revealing that key problems are NP-complete or PP-hard, indicating significant intractability in this area.

## Contribution

It establishes the NP-completeness and PP-hardness of fundamental query evaluation problems related to itemset frequencies, highlighting their computational intractability.

## Key findings

- Checking maximal consistent frequency is NP-complete
- Evaluating Maximum Entropy estimate is PP-hard
- Checking consistency is NP-complete

## Abstract

We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intractable. We show that despite the limitations our problems are also intractable, namely, we show that checking whether the maximal consistent frequency of a query is larger than a given threshold is NP-complete and that evaluating the Maximum Entropy estimate of a query is PP-hard. We also prove that checking consistency is NP-complete.