Ranking and Drawing in Subexponential Time
Identifieur interne : 000949 ( Main/Exploration ); précédent : 000948; suivant : 000950Ranking and Drawing in Subexponential Time
Auteurs : Henning Fernau [Allemagne] ; Fedor V. Fomin [Norvège] ; Daniel Lokshtanov [Norvège] ; Matthias Mnich [Pays-Bas] ; Geevarghese Philip [Inde] ; Saket Saurabh [Inde]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2011.
Abstract
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 $\mathcal{O}^{*}(2^{\mathcal{O}(\sqrt{k}{\rm log} k)})$ , where k is the parameter, and significantly improve the previous best algorithms with running times $\cal{O}^{*}$ (1.403 k ) and $\cal{O}^{*}$ (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 $\mathcal{O}^{*}(2^{\mathcal{O}(\sqrt{k}{\rm log} k)})$ , 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]).
Url:
DOI: 10.1007/978-3-642-19222-7_34
Affiliations:
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Fomin</name><affiliation wicri:level="1"><country xml:lang="fr">Norvège</country><wicri:regionArea>Department of Informatics, University of Bergen, 5020, Bergen</wicri:regionArea><wicri:noRegion>Bergen</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Norvège</country></affiliation></author><author><name sortKey="Lokshtanov, Daniel" sort="Lokshtanov, Daniel" uniqKey="Lokshtanov D" first="Daniel" last="Lokshtanov">Daniel Lokshtanov</name><affiliation wicri:level="1"><country xml:lang="fr">Norvège</country><wicri:regionArea>Department of Informatics, University of Bergen, 5020, Bergen</wicri:regionArea><wicri:noRegion>Bergen</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Norvège</country></affiliation></author><author><name sortKey="Mnich, Matthias" sort="Mnich, Matthias" uniqKey="Mnich M" first="Matthias" last="Mnich">Matthias Mnich</name><affiliation wicri:level="1"><country xml:lang="fr">Pays-Bas</country><wicri:regionArea>Eindhoven University of Technology, Eindhoven</wicri:regionArea><wicri:noRegion>Eindhoven</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Pays-Bas</country></affiliation></author><author><name sortKey="Philip, Geevarghese" sort="Philip, Geevarghese" uniqKey="Philip G" first="Geevarghese" last="Philip">Geevarghese Philip</name><affiliation wicri:level="1"><country xml:lang="fr">Inde</country><wicri:regionArea>The Institute of Mathematical Sciences, Taramani, 600 113, Chennai</wicri:regionArea><wicri:noRegion>Chennai</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Inde</country></affiliation></author><author><name sortKey="Saurabh, Saket" sort="Saurabh, Saket" uniqKey="Saurabh S" first="Saket" last="Saurabh">Saket Saurabh</name><affiliation wicri:level="1"><country xml:lang="fr">Inde</country><wicri:regionArea>The Institute of Mathematical Sciences, Taramani, 600 113, Chennai</wicri:regionArea><wicri:noRegion>Chennai</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Inde</country></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><imprint><date>2011</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">54CF86FA7D9FF5D7596EBBD629923242C0567E4F</idno><idno type="DOI">10.1007/978-3-642-19222-7_34</idno><idno type="ChapterID">34</idno><idno type="ChapterID">Chap34</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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 $\mathcal{O}^{*}(2^{\mathcal{O}(\sqrt{k}{\rm log} k)})$ , where k is the parameter, and significantly improve the previous best algorithms with running times $\cal{O}^{*}$ (1.403 k ) and $\cal{O}^{*}$ (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 $\mathcal{O}^{*}(2^{\mathcal{O}(\sqrt{k}{\rm log} k)})$ , 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]).</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>Inde</li><li>Norvège</li><li>Pays-Bas</li></country><region><li>Rhénanie-Palatinat</li></region><settlement><li>Trèves (Allemagne)</li></settlement><orgName><li>Université de Trèves</li></orgName></list><tree><country name="Allemagne"><region name="Rhénanie-Palatinat"><name sortKey="Fernau, Henning" sort="Fernau, Henning" uniqKey="Fernau H" first="Henning" last="Fernau">Henning Fernau</name></region><name sortKey="Fernau, Henning" sort="Fernau, Henning" uniqKey="Fernau H" first="Henning" last="Fernau">Henning Fernau</name></country><country name="Norvège"><noRegion><name sortKey="Fomin, Fedor V" sort="Fomin, Fedor V" uniqKey="Fomin F" first="Fedor V." last="Fomin">Fedor V. Fomin</name></noRegion><name sortKey="Fomin, Fedor V" sort="Fomin, Fedor V" uniqKey="Fomin F" first="Fedor V." last="Fomin">Fedor V. 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