Complexity Results for Preference Aggregation over (m)CP-nets: Pareto and Majority Voting
Combinatorial preference aggregation has many applications in AI. Given the exponential nature of these preferences, compact representations are needed and ($m$)CP-nets are among the most studied ones. Sequential and global voting are two ways to aggregate preferences over CP-nets. In the former, preferences are aggregated feature-by-feature. Hence, when preferences have specific feature dependencies, sequential voting may exhibit voting paradoxes, i.e., it might select sub-optimal outcomes. To avoid paradoxes in sequential voting, one has often assumed the $\mathcal{O}$-legality restriction, which imposes a shared topological order among all the CP-nets. On the contrary, in global voting, CP-nets are considered as a whole during preference aggregation. For this reason, global voting is immune from paradoxes, and there is no need to impose restrictions over the CP-nets' topological structure. Sequential voting over $\mathcal{O}$-legal CP-nets has extensively been investigated. On the other hand, global voting over non-$\mathcal{O}$-legal CP-nets has not carefully been analyzed, despite it was stated in the literature that a theoretical comparison between global and sequential voting was promising and a precise complexity analysis for global voting has been asked for multiple times. In quite few works, very partial results on the complexity of global voting over CP-nets have been given. We start to fill this gap by carrying out a thorough complexity analysis of Pareto and majority global voting over not necessarily $\mathcal{O}$-legal acyclic binary polynomially connected (m)CP-nets. We settle these problems in the polynomial hierarchy, and some of them in PTIME or LOGSPACE, whereas EXPTIME was the previously known upper bound for most of them. We show various tight lower bounds and matching upper bounds for problems that up to date did not have any explicit non-obvious lower bound.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Encoding monotonic multi-set preferences using CI-nets: preliminary report
CP-nets and their variants constitute one of the main AI approaches for specifying and reasoning about preferences. CI-nets, in particular, are a CP-inspired formalism for representing ordinal preferences over sets of go…
Approximation Algorithms for Preference Aggregation Using CP-Nets
This paper studies the design and analysis of approximation algorithms for aggregating preferences over combinatorial domains, represented using Conditional Preference Networks (CP-nets). Its focus is on aggregating pref…
The Complexity of Learning Acyclic Conditional Preference Networks
Learning of user preferences, as represented by, for example, Conditional Preference Networks (CP-nets), has become a core issue in AI research. Recent studies investigate learning of CP-nets from randomly chosen example…
AttributeThe Computational Complexity of Dominance and Consistency in CP-Nets
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 …
An extended Knowledge Compilation Map for Conditional Preference Statements-based and Generalized Additive Utilities-based Languages
Conditional preference statements have been used to compactly represent preferences over combinatorial domains. They are at the core of CP-nets and their generalizations, and lexicographic preference trees. Several works…