Parameterized Complexity of Multi-winner Determination: More Effort Towards Fixed-Parameter Tractability

TL;DR

This paper investigates the parameterized complexity of multi-winner determination problems for three common approval voting rules, exploring new parameters and structural aspects to identify fixed-parameter tractability.

Contribution

It introduces new parameterizations and structural considerations to analyze the fixed-parameter tractability of winner determination problems under MAV, PAV, and CCAV.

Findings

Identifies parameter combinations leading to fixed-parameter tractability

Provides complexity classifications for various parameters

Revisits known problems with new analytical approaches

Abstract

We study the parameterized complexity of winner determination problems for three prevalent $k$-committee selection rules, namely the minimax approval voting (MAV), the proportional approval voting (PAV), and the Chamberlin-Courant's approval voting (CCAV). It is known that these problems are computationally hard. Although they have been studied from the parameterized complexity point of view with respect to several natural parameters, many of them turned out to be W[1]-hard or W[2]-hard. Aiming at obtaining plentiful fixed-parameter algorithms, we revisit these problems by considering more natural single parameters, combined parameters, and structural parameters.