Approximation Algorithms for Preference Aggregation Using CP-Nets

TL;DR

This paper develops and analyzes approximation algorithms for preference aggregation over CP-nets, achieving better ratios than previous methods and providing optimal solutions for certain instances.

Contribution

Introduces a polynomial-time approximation algorithm for CP-net preference aggregation with improved approximation ratios and optimal solutions for specific cases.

Findings

A trivial 2-approximation algorithm analyzed and improved under certain conditions.

Proposed polynomial-time algorithm often outperforms the trivial approach.

Identified problem instances where the new algorithm yields optimal solutions.

Abstract

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 preferences over so-called \emph{swaps}, for which optimal solutions in general are already known to be of exponential size. We first analyze a trivial 2-approximation algorithm that simply outputs the best of the given input preferences, and establish a structural condition under which the approximation ratio of this algorithm is improved to $4/3$. We then propose a polynomial-time approximation algorithm whose outputs are provably no worse than those of the trivial algorithm, but often substantially better. A family of problem instances is presented for which our improved algorithm produces optimal solutions, while, for any $\varepsilon$, the trivial algorithm can\emph{not}\/ attain a $(2-\varepsilon)$-approximation. These results may lead to the first polynomial-time approximation algorithm that solves the CP-net aggregation problem for swaps with an approximation ratio substantially better than $2$.