Abstract
Winner determination problem under Chamberlin-Courant system deals with the problem of selecting a fixed-size assembly from a set of candidates that minimizes the sum of misrepresentation values. This system does not restrict the candidates to have a minimum number of votes to be selected. The problem is known to be NP-hard. In this paper, we consider domination analysis of a 2-Opt heuristic for this problem. We show that the 2-Opt heuristic produces solutions no worse than the average solution in polynomial time. We also show that the domination number of the 2-Opt heuristic is at least \({m-1 \atopwithdelims ()k-1}k^{n-1}\) for n voters and m candidates.
E. Iranmanesh and R. Krishnamurti—Supported by NSERC Discovery Grant, Canada.
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Acknowledgements
We wish to thank Abraham Punnen, Binay Bhattacharya, Kamyar Khodamoradi, and Vladyslav Sokol, for helpful discussions on this problem. The authors acknowledge support from a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant.
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Ćustić, A., Iranmanesh, E., Krishnamurti, R. (2017). Analysis of 2-Opt Heuristic for the Winner Determination Problem Under the Chamberlin-Courant System. In: Gaur, D., Narayanaswamy, N. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2017. Lecture Notes in Computer Science(), vol 10156. Springer, Cham. https://doi.org/10.1007/978-3-319-53007-9_10
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