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

@article{Yang2018ParameterizedCO, title={Parameterized Complexity of Multi-winner Determination: More Effort Towards Fixed-Parameter Tractability}, author={Yongjie Yang and Jianxin Wang}, journal={ArXiv}, year={2018}, volume={abs/2107.04685} }

We study the k -committee selection rules minimax approval, proportional approval, and Chamberlin-Courant's approval. It is known that WINNER DETERMINATION for these rules is NP-hard. Moreover, the parameterized complexity of the problem has also been studied with respect to some natural parameters. However, there are still numerous parameterizations that have not been considered. We revisit the parameterized complexity of WINNER DETERMINATION for these rules by considering several important…

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## References

SHOWING 1-10 OF 67 REFERENCES

Parameterized Complexity of Winner Determination in Minimax Committee Elections

- Computer ScienceAAMAS
- 2016

It is proved that on both linear and partial orders, it is W[2]-hard to determine the winners with respect to the size of the committee, and it is shown that in several special settings, the winner determination problem of a minimax approval committee election is polynomial-time solvable.

Single-Peakedness and Total Unimodularity: New Polynomial-Time Algorithms for Multi-Winner Elections

- Computer ScienceAAAI
- 2018

This technique gives efficient algorithms for finding optimal committees under Proportional Approval Voting (PAV) and the Chamberlin–Courant rule with single-peaked preferences, as well as for certain OWA-based rules.

On the Complexity of Destructive Bribery in Approval-Based Multi-winner Voting

- Computer ScienceAAMAS
- 2020

This paper explores the complexity of several destructive bribery problems under five prestigious approval-based multi-winner voting rules, and for NP-hard problems the authors study their parameterized complexity with respect to meaningful parameters.

The control complexity of r-Approval: From the single-peaked case to the general case

- Mathematics, Computer ScienceJ. Comput. Syst. Sci.
- 2017

It turns out that most NP-completeness results in general also hold in k-peaked elections, even for k=2,3, and the problems are studied from the viewpoint of parameterized complexity and achieve both FPT and W-hardness results.

On the Parameterized Complexity of Minimax Approval Voting

- Computer ScienceAAMAS
- 2015

It is demonstrated that the problem is W[2]-hard when parameterized by the size of the committee to be chosen, but does admit a FPT algorithm when parameterizing by the number of strings that is more efficient than the previous ILP-based approaches for the problem.

Complexity of Manipulating and Controlling Approval-Based Multiwinner Voting

- Computer ScienceIJCAI
- 2019

It is shown that six prevalent approvalbased multiwinner voting rules generally resist the proposed strategic types and fixed-parameter tractability results for these problems with respect to several natural parameters and derive polynomial-time algorithms for certain special cases.

On the Computation of Fully Proportional Representation

- Computer ScienceJ. Artif. Intell. Res.
- 2013

This work investigates two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe and investigates the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters.

Fixed-Parameter Tractability and Completeness II: On Completeness for W[1]

- Computer Science, MathematicsTheor. Comput. Sci.
- 1995

This work shows that INDEPENDENT SET is complete for W, and the W Hierarchy of parameterized problems was defined, and complete problems were identified for the classes W [ t ] for t ⩾ 2.

Fixed Parameter Tractability and Completeness

- Mathematics, Computer ScienceComplexity Theory: Current Research
- 1992

It is shown that if Dominating Set is fixed-parameter tractable, then so are a variety of parameterized problems, such as Independent Set, and that for this problem, and for the problem of determining whether a graph has k disjoint cycles, it may take c = 1.

Multi-Winner Elections: Complexity of Manipulation, Control and Winner-Determination

- Computer ScienceIJCAI
- 2007

This paper fully characterize the worst-case complexity of manipulation and control in the context of four prominent multi-winner voting systems, and shows that several tailor-made multi-winning voting schemes are impractical, as it is NP-hard to select the winners in these schemes.