@inproceedings{6350fae694344daaa735a92048ca0ad9,

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 \mathcal{o}^{*}(2^{\mathcal{o}(\sqrt{k}{\rm log} k)})\mathcal{o}^{*}(2^{\mathcal{o}(\sqrt{k}{\rm log} k)}), where k is the parameter, and significantly improve the previous best algorithms with running times \cal{o}^{*}\cal{o}^{*}(1.403 k ) and \cal{o}^{*}\cal{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 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 \mathcal{o}^{*}(2^{\mathcal{o}(\sqrt{k}{\rm log} k)})\mathcal{o}^{*}(2^{\mathcal{o}(\sqrt{k}{\rm 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 = "Henning Fernau and Fomin, {Fedor V.} and Daniel Lokshtanov and Matthias Mnich and Geevarghese Philip and Saket 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 = "Iliopoulos, {Costas S.} and Smyth, {William F.}",

booktitle = "Combinatorial Algorithms",

address = "United States",

}