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

arXiv: https://arxiv.org/abs/2107.04685 · HTML: https://mlsanity.com/paper/2107.04685/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2021.

## Built on by (most cited first, 4 of 4)

- [Multiwinner Temporal Voting with Aversion to Change](https://mlsanity.com/paper/2408.11017/) (2024)
- [DiRe Committee : Diversity and Representation Constraints in Multiwinner Elections](https://mlsanity.com/paper/2107.07356/) (2021)
- [Polynomial-Time Algorithm for Thiele Voting Rules with Voter Interval Preferences](https://mlsanity.com/paper/2604.05953/) (2026)
- [Algorithms for Structured Elections under Thiele Voting Rules](https://mlsanity.com/paper/2607.28575/) (2026)

## Abstract (arXiv)

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.