Chamberlin--Courant Rule with Approval Ballots: Approximating the MaxCover Problem with Bounded Frequencies in FPT Time
Piotr Skowron,Piotr Faliszewski +1 more
Reads0
Chats0
TLDR
This work considers the problem of winner determination under Chamberlin-Courant's multiwinner voting rule with approval utilities and shows exponential-time/FPT approximation algorithms that achieve arbitrarily good approximation ratios and have running times much better than known exact algorithms.Abstract:
We consider the problem of winner determination under Chamberlin--Courant's multiwinner voting rule with approval utilities. This problem is equivalent to the well-known NP-complete MaxCover problem and, so, the best polynomial-time approximation algorithm for it has approximation ratio 1 - 1/e. We show exponential-time/FPT approximation algorithms that, on one hand, achieve arbitrarily good approximation ratios and, on the other hand, have running times much better than known exact algorithms. We focus on the cases where the voters have to approve of at most/at least a given number of candidates.read more
Citations
More filters
Posted Content
Properties of Multiwinner Voting Rules
TL;DR: This paper considers committee selection rules that can be viewed as generalizations of single-winner scoring rules, including SNTV, Bloc, k-Borda, STV, as well as several variants of the Chamberlin–Courant rule and the Monroe rule and their approximations.
Proceedings Article
Finding a collective set of items: from proportional multirepresentation to group recommendation
TL;DR: The problem is hard in general, but a number of tractability results for its natural special cases are shown.
Journal ArticleDOI
Achieving fully proportional representation
TL;DR: In this paper, the complexity of winner determination under the Monroe and Chamberlin-Courant multiwinner voting rules was studied, where the total satisfaction or dissatisfaction of the voters with their representatives is calculated either as the sum of individual (dis)satisfactions in the utilitarian case or as the (dis)-satisfaction of the worst off voter in the egalitarian case.
Journal ArticleDOI
The complexity of fully proportional representation for single-crossing electorates
TL;DR: The authors' algorithm for Chamberlin-Courant's rule can be modified to work for elections with bounded single-crossing width, and has considerably better worst-case running time than that of Betzler et al.
References
More filters
Book
Approximation Algorithms
TL;DR: Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field.
Book
Parameterized Complexity
TL;DR: An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability, and introduces readers to new classes of algorithms which may be analysed more precisely than was the case until now.
Book
Parameterized complexity theory
Jörg Flum,Martin Grohe +1 more
TL;DR: Fixed-Parameter Tractability.
Book
Invitation to fixed-parameter algorithms
TL;DR: This paper discusses Fixed-Parameter Algorithms, Parameterized Complexity Theory, and Selected Case Studies, and some of the techniques used in this work.
Book
Parameterized Algorithms
Marek Cygan,Fedor V. Fomin,Lukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh +7 more
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.