Limits of Preprocessing

TL;DR

This paper provides a theoretical boundary on the effectiveness of polynomial-time preprocessing for key AI problems, showing that under certain assumptions, such preprocessing cannot significantly reduce problem sizes.

Contribution

It offers the first theoretical analysis demonstrating limits of polynomial-time preprocessing for various AI problems, establishing boundaries based on complexity assumptions.

Findings

Polynomial-time preprocessing cannot produce polynomial kernels for the considered problems.

Results apply to problems like Constraint Satisfaction, Satisfiability, and Bayesian Reasoning.

Provides a complexity-theoretic boundary for preprocessing effectiveness.

Abstract

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability, Nonmonotonic and Bayesian Reasoning. We show that, subject to a complexity theoretic assumption, none of the considered problems can be reduced by polynomial-time preprocessing to a problem kernel whose size is polynomial in a structural problem parameter of the input, such as induced width or backdoor size. Our results provide a firm theoretical boundary for the performance of polynomial-time preprocessing algorithms for the considered problems.