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The Computational Complexity of Dominance and Consistency in CP-Nets (1401.3453v1)

Published 15 Jan 2014 in cs.AI

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.

Citations (179)

Summary

  • The paper establishes that both dominance and consistency testing in CP-Nets are PSPACE-complete, highlighting significant computational complexity.
  • It reduces these problems from propositional STRIPS planning, connecting planning frameworks with preference reasoning.
  • The findings prompt a reevaluation of CP-net applications in real-time decision-making, suggesting the use of heuristics to mitigate computational burdens.

Computational Complexity of Dominance and Consistency in CP-Nets

The paper "The Computational Complexity of Dominance and Consistency in CP-Nets" by Judy Goldsmith et al. provides a thorough examination of the computational complexity associated with dominance and consistency testing within CP-nets, expanding on earlier work limited to subclasses characterized by acyclic dependency graphs. The authors establish that both dominance and consistency testing within general forms of CP-nets present PSPACE-complete problems, elucidating the inherent computational challenges this complex preference representation entails.

Central to the findings of this paper is the reduction of these complexity issues from propositional STRIPS planning, a correlation that reinforces the relationship between planning and preference reasoning frameworks. This reduction to PSPACE-complete problems implies that checking dominance or consistency in CP-nets can be computationally intensive, even rendering inherently complex scenarios where dependency graphs are cyclic. The exploration involves assessing numerous notions such as strong dominance, dominance equivalence, and others, culminating in a comprehensive analysis of the complexity implications across various decision problems linked to CP-nets and GCP-nets.

For researchers focused on the computational aspects of preference modeling, these results highlight key challenges that arise from attempting to utilize CP-nets in practical applications such as automated planning and decision-making systems. Given the PSPACE-completeness results, applications involving CP-nets must account for significant computational resource requirements when testing dominance or searching for consistent preference models. This computational burden suggests the necessity for using heuristics or approximations in real-world applications to provide viable solutions within reasonable timeframes.

Significant findings of the paper, such as the NP-completeness results concerning the existence of optimal solutions, prompt a reevaluation of previous assumptions regarding the capacity to integrate CP-nets in domains demanding real-time decision-making. While the theoretical insights provided in this paper underscore the formal challenges, they simultaneously suggest potential pathways for future research—particularly those seeking efficient algorithms or restriction classes to mitigate these complexity barriers. Extending CP-nets with potential optimizations present vibrant avenues for exploration.

Moreover, the implications go beyond academic discourse, suggesting practical concerns such as integrating CP-nets in AI systems sensitive to decision-making efficiency. The relationship between CP-net representations and STRIPS planning opens up possibilities for adapting robust planning mechanisms, enhancing the computational tractability of preference management models.

In summary, Goldsmith et al.'s work advances knowledge narrowly situated at the border between preference logic and computational complexity. It poses valuable inquiries for the AI community, stimulating research on computational efficiency improvements within preference models and asserting an exigent call for novel frameworks that can realistically navigate these complexity-induced challenges in dynamic environments.