@inproceedings{ba78587421ee4c6c8b97a121a40c7478,

title = "Ranking and drawing in subexponential time",

abstract = "In 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*(2^{O(\sqrt{k} log k)}), where k is the parameter, and significantly improve the previous best algorithms with running times O*(1.403^k) and O*(1.4656^k), 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 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*(2^{O(\sqrt{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]).",

author = "H. Fernau and F.V. Fomin and D. Lokshtanov and M. Mnich and G. Philip and S. Saurabh",

year = "2011",

doi = "10.1007/978-3-642-19222-7_34",

language = "English",

isbn = "978-3-642-19221-0",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "337--348",

editor = "C.S. Iliopoulos and W.F. Smyth",

booktitle = "Combinatorial Algorithms (21st International Workshop, IWOCA '10, London, UK, July 26-28, 2010. Proceedings)",

}