The Computational Complexity of Dominance and Consistency in CP-Nets

TL;DR

This paper analyzes the computational complexity of testing dominance and consistency in general CP-nets, revealing that these problems are PSPACE-complete, and explores related concepts like strong dominance and optimality.

Contribution

It extends the complexity analysis of CP-net dominance and consistency to cyclic dependency graphs, establishing PSPACE-completeness for general CP-nets and connecting to STRIPS planning.

Findings

Dominance and consistency in general CP-nets are PSPACE-complete.

Complexity results apply to cyclic dependency graphs in CP-nets.

Reductions from STRIPS planning reinforce the connection between preference reasoning and planning.

Abstract

We investigate the computational complexity of testing dominance and consistency in CP-nets. Previously, the complexity of dominance has been determined for restricted classes in which the dependency graph of the CP-net is acyclic. However, there are preferences of interest that define cyclic dependency graphs; these are modeled with general CP-nets. In our main results, we show here that both dominance and consistency for general CP-nets are PSPACE-complete. We then consider the concept of strong dominance, dominance equivalence and dominance incomparability, and several notions of optimality, and identify the complexity of the corresponding decision problems. The reductions used in the proofs are from STRIPS planning, and thus reinforce the earlier established connections between both areas.