Ranking and drawing in subexponential time

  • Authors:

  • Henning Fernau;Fedor V. Fomin;Daniel Lokshtanov;Matthias Mnich;Geevarghese Philip;Saket Saurabh

  • Affiliations:

  • Universität Trier FB 4-Abteilung Informatik, Trier, Germany;Department of Informatics, University of Bergen, Bergen, Norway;Department of Informatics, University of Bergen, Bergen, Norway;Eindhoven University of Technology, Eindhoven, The Netherlands;The Institute of Mathematical Sciences, Taramani, Chennai, India;The Institute of Mathematical Sciences, Taramani, Chennai, India

  • Venue:
  • IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
  • Year:
  • 2010

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Abstract

IIn this paper we obtain parameterized subexponential-time algorithms for p-KEMENY AGGREGATION (p-KAGG) -- a problem in social choice theory -- and for p-ONE-SIDED CROSSING MINIMIZATION (p-OSCM) - a problem in graph drawing (see the introduction for definitions). These algorithms run in time O*(2O(√k log k)), 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(√k log k)), 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]).