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Open Access

Social Choice Meets Graph Drawing: How to Get Subexponential Time Algorithms for Ranking and Drawing Problems

FB 4—Abteilung Informatikwissenschaften, Universität Trier, D-54286 Trier, Germany.
Department of Informatics, University of Bergen, N-5020 Bergen, Norway.
Max-Planck-Institut für Informatik, D-66123 Saarbrücken, Germany.
Institute of Mathematical Sciences, Chennai - 600113, India.
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Abstract

We analyze a common feature of p-Kemeny AGGregation ( p-KAGG) and p-One-Sided Crossing Minimization ( p-OSCM) to provide new insights and findings of interest to both the graph drawing community and the social choice community. We obtain parameterized subexponential-time algorithms for p-KAGG—a problem in social choice theory—and for p-OSCM—a problem in graph drawing. These algorithms run in time O*(2O(klogk)), where k is the parameter, and significantly improve the previous best algorithms with running times 𝒪*(1.403k) and 𝒪*(1.4656k), respectively. We also study natural "above-guarantee" versions of these problems and show them to be fixed parameter tractable. In fact, we show that the above-guarantee versions of these problems are equivalent to a weighted variant of p-directed feedback arc set. Our results for the above-guarantee version of p-KAGG reveal an interesting contrast. We show that when the number of "votes" in the input to p-KAGG is odd the above guarantee version can still be solved in time O*(2O(klogk)), while if it is even then the problem cannot have a subexponential time algorithm unless the exponential time hypothesis fails (equivalently, unless FPT=M[1]).

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Tsinghua Science and Technology
Pages 374-386
Cite this article:
Fernau H, Fomin FV, Lokshtanov D, et al. Social Choice Meets Graph Drawing: How to Get Subexponential Time Algorithms for Ranking and Drawing Problems. Tsinghua Science and Technology, 2014, 19(4): 374-386. https://doi.org/10.1109/TST.2014.6867519

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Received: 22 June 2014
Accepted: 04 July 2014
Published: 30 July 2014
© The author(s) 2014
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