Planar 3-SAT with a clause/variable cycle

Alexander Pilz

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

Abstract

In the Planar 3-SAT problem, we are given a 3-SAT formula together with its incidence graph, which is planar, and are asked whether this formula is satisfiable. Since Lichtenstein’s proof that this problem is NP-complete, it has been used as a starting point for a large number of reductions. In the course of this research, di erent restrictions on the incidence graph of the formula have been devised, for which the problem also remains hard. In this paper, we investigate the restriction in which we require that the incidence graph is augmented by the edges of a Hamiltonian cycle that first passes through all variables and then through all clauses, in a way that the resulting graph is still planar. We show that the problem of deciding satisfiability of a 3-SAT formula remains NP-complete even if the incidence graph is restricted in that way and the Hamiltonian cycle is given. This complements previous results demanding cycles only through either the variables or clauses. The problem remains hard for monotone formulas and instances with exactly three distinct variables per clause. In the course of this investigation, we show that monotone instances of Planar 3-SAT with three distinct variables per clause are always satisfiable, thus settling the question by Darmann, Döcker, and Dorn on the complexity of this problem variant in a surprising way.

Originalspracheenglisch
Titel16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018
Herausgeber (Verlag)Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH
Seiten311-3113
Seitenumfang2803
Band101
ISBN (elektronisch)9783959770682
DOIs
PublikationsstatusVeröffentlicht - 1 Jun 2018
Extern publiziertJa
Veranstaltung16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018 - Malmo, Schweden
Dauer: 18 Jun 201820 Jun 2018

Konferenz

Konferenz16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018
LandSchweden
OrtMalmo
Zeitraum18/06/1820/06/18

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    ASJC Scopus subject areas

    • Software

    Dieses zitieren

    Pilz, A. (2018). Planar 3-SAT with a clause/variable cycle. in 16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018 (Band 101, S. 311-3113). Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH. https://doi.org/10.4230/LIPIcs.SWAT.2018.31