Determining the Winner of a Dodgson Election is Hard

Fellows, Michael; Jansen, Bart M. P.; Lokshtanov, Daniel; Rosamond, Frances A.; Saurabh, Saket

doi:10.4230/LIPIcs.FSTTCS.2010.459

Document

Determining the Winner of a Dodgson Election is Hard

Authors Michael Fellows, Bart M. P. Jansen, Daniel Lokshtanov, Frances A. Rosamond, Saket Saurabh

Part of: Volume: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2010-12-14

PDF

File

PDF

LIPIcs.FSTTCS.2010.459.pdf

Filesize: 447 kB
10 pages

Document Identifiers

DOI: 10.4230/LIPIcs.FSTTCS.2010.459
URN: urn:nbn:de:0030-drops-28866

Subject Classification

Keywords

Dodgson Score
Parameterized Complexity
Kernelization Lower Bounds

Metrics

Access Statistics
Total Accesses (updated on a weekly basis)

0

PDF Downloads

0

Metadata Views

Abstract

Computing the Dodgson Score of a candidate in an election is a hard computational problem, which has been analyzed using classical and parameterized analysis. In this paper we resolve two open problems regarding the parameterized complexity of DODGSON SCORE. We show that DODGSON SCORE parameterized by the target score value $k$ does not have a polynomial kernel unless the polynomial hierarchy collapses to the third level; this complements a result of Fellows, Rosamond and Slinko who obtain a non-trivial kernel of exponential size for a generalization of this problem. We also prove that DODGSON SCORE parameterized by the number $n$ of votes is hard for $W[1]$.

Cite As Get BibTex

Michael Fellows, Bart M. P. Jansen, Daniel Lokshtanov, Frances A. Rosamond, and Saket Saurabh. Determining the Winner of a Dodgson Election is Hard. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 459-468, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010) https://doi.org/10.4230/LIPIcs.FSTTCS.2010.459

Author Details

Michael Fellows

Bart M. P. Jansen

Daniel Lokshtanov

Frances A. Rosamond

Saket Saurabh

Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail