computer science publication server: No conditions. Results ordered -Date Deposited. 2021-04-23T00:07:12ZEPrintshttp://e-archive.informatik.uni-koeln.de/images/sitelogo.pnghttp://e-archive.informatik.uni-koeln.de/2013-05-03T07:03:27Z2013-05-03T07:03:27Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/698This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/6982013-05-03T07:03:27ZEffectiveness of pre- and inprocessing for CDCL-based SAT solvingApplying pre- and inprocessing techniques to simplify CNF formulas both before and during search can considerably improve the performance of modern SAT solvers. These algorithms mostly aim at reducing the number of clauses, literals, and variables in the formula. However, to be worthwhile, it is necessary that their additional runtime does not exceed the runtime saved during the subsequent SAT solver execution. In this paper we investigate the efficiency and the practicability of selected simplification algorithms for CDCL-based SAT solving. We first analyze them by means of their expected impact on the CNF formula and SAT solving at all. While testing them on real-world and combinatorial SAT instances, we show which techniques and combinations of them yield a desirable speedup and which ones should be avoided.Andreas WotzlawWotzlaw, AndreasAlexander van der Grintenvan der Grinten, AlexanderEwald SpeckenmeyerSpeckenmeyer, Ewald2013-01-17T13:09:31Z2013-01-17T13:09:31Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/693This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/6932013-01-17T13:09:31ZA Satisfiability-based Approach for Generalized Tanglegrams on Level Graphs
A tanglegram is a pair of (not necessarily binary) trees on the same set of leaves with matching leaves in the two trees joined by an edge. Tanglegrams are widely used in computational biology to compare evolutionary histories of species. In this work we present a formulation of two related combinatorial embedding problems concerning tanglegrams in terms of CNF-formulas. The first problem is known as the planar embedding and the second as the crossing minimization problem. We show that our satisfiability-based encoding of these problems can handle a much more general case with more than two, not necessarily binary or complete, trees defined on arbitrary sets of leaves and allowed to vary their layouts. Furthermore, we present an experimental comparison of our technique and several known heuristics for solving generalized binary tanglegrams, showing its competitive performance and efficiency and thus proving its practical usability.
Andreas WotzlawWotzlaw, AndreasEwald SpeckenmeyerSpeckenmeyer, EwaldStefan PorschenPorschen, Stefan2012-06-26T09:49:02Z2012-06-26T09:49:02Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/683This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/6832012-06-26T09:49:02ZsatUZK: Solver DescriptionAlexander van der Grintenvan der Grinten, AlexanderAndreas WotzlawWotzlaw, AndreasEwald SpeckenmeyerSpeckenmeyer, EwaldStefan PorschenPorschen, Stefan2012-06-26T09:44:33Z2012-06-26T09:44:33Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/684This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/6842012-06-26T09:44:33ZpfolioUZK: Solver DescriptionAndreas WotzlawWotzlaw, AndreasAlexander van der Grintenvan der Grinten, AlexanderEwald SpeckenmeyerSpeckenmeyer, EwaldStefan PorschenPorschen, Stefan2012-03-29T14:11:30Z2012-03-29T14:11:30Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/678This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/6782012-03-29T14:11:30ZProbabilistic Analysis of Random Mixed Horn Formulas
We present a probabilistic analysis of random mixed Horn formulas (MHF), i.e., formulas in conjunctive normal form consisting of a positive monotone part of quadratic clauses and a part of Horn clauses, with m clauses, n variables, and up to n literals per Horn clause. For MHFs parameterized by n and m with uniform distribution of instances and for large n, we derive upper bounds for the expected number of models. For the class of random negative MHFs, where only monotone negative Horn clauses are allowed to occur, we give a lower bound for the probability that formulas from this class are satisfiable. We expect that the model studied theoretically here may be of interest for the determination of hard instances, which are conjectured to be found in the transition area from satisfiability to unsatisfiability of the instances from the parameterized classes of formulas.Andreas WotzlawWotzlaw, AndreasEwald SpeckenmeyerSpeckenmeyer, EwaldStefan PorschenPorschen, Stefan2011-10-21T12:32:25Z2015-11-24T12:11:30Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/632This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/6322011-10-21T12:32:25ZXSAT and NAE-SAT of linear CNF classesXSAT and NAE-SAT are important variants of the propositional
satisfiability problem (SAT). Both are studied here regarding their computational complexity of linear CNF formulas. We prove that
both variants remain NP-complete for (monotone) linear formulas
yielding the conclusion that also bicolorability of linear hypergraphs is NP-complete. The reduction used gives rise to the complexity investigation of both variants for several monotone linear subclasses that are parameterized by the size of clauses or by the number of
occurrences of variables. In particular cases of these parameter values we are able to verify the NP-completeness of XSAT
respectively NAE-SAT; though we cannot provide a complete treatment. Finally we focus on exact linear formulas where clauses intersect pairwise, and for which SAT is known to be polynomial-time solvable. We verify the same assertion for NAE-SAT relying on some well-known result; whereas we obtain NP-completeness for XSAT of exact linear formulas. The case of uniform clause size k remains open for the latter problem. However, we can provide its polynomial-time behavior for k at most 6.Stefan PorschenPorschen, StefanTatjana SchmidtSchmidt, TatjanaEwald SpeckenmeyerSpeckenmeyer, EwaldAndreas WotzlawWotzlaw, Andreas2011-10-13T14:52:11Z2012-11-08T13:46:27Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/631This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/6312011-10-13T14:52:11ZGeneralized k-ary tanglegrams on level graphs: a satisfiability-based approach and its evaluationA tanglegram is a pair of (not necessarily binary) trees on the same set of leaves with matching leaves in the two trees joined by an edge. Tanglegrams are widely used in computational biology to compare evolutionary histories of species. In this work we present a
formulation of two related combinatorial embedding problems concerning tanglegrams in terms of CNF-formulas. The first problem is known as the planar embedding and the second as the crossing minimization problem. We show that our satisfiability-base encoding of these problems can handle a much more general case with more than two, not
necessarily binary or complete, trees defined on arbitrary sets of
leaves and allowed to vary their layouts. Furthermore, we present an experimental comparison of our technique and several known heuristics for solving generalized binary tanglegrams, showing its competitive
performance and efficiency and thus proving its practical usability.Andreas WotzlawWotzlaw, AndreasEwald SpeckenmeyerSpeckenmeyer, EwaldStefan PorschenPorschen, Stefan2011-02-23T00:00:00Z2012-01-09T12:06:49Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/614This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/6142011-02-23T00:00:00ZA Satisfiability-based Approach for Embedding Generalized Tanglegrams on Level GraphsA tanglegram is a pair of trees on the same set of leaves with matching leaves in the two trees joined by an edge. Tanglegrams are widely used in computational biology to compare evolutionary histories of species. In this paper we present a formulation of two related combinatorial embedding problems concerning tanglegrams in terms of CNF-formulas. The first problem is known as planar embedding and the second as crossing minimization problem. We show that our satisfiability formulation of these problems can handle a much more general case with more than two, not necessarily binary or complete, trees defined on arbitrary sets of leaves and allowed to vary their layouts.Ewald SpeckenmeyerSpeckenmeyer, EwaldAndreas WotzlawWotzlaw, AndreasStefan PorschenPorschen, Stefan2007-04-19T00:00:00Z2011-12-19T09:44:59Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/526This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5262007-04-19T00:00:00ZOn variable-weighted exact satisfiability problemsWe show that the NP-hard optimization problems minimum and maximum weight exact satisfiability (XSAT) for a CNF formula C over n propositional variables equipped with arbitrary real-valued weights can be solved in O(|C|2^{0.2441n}) time. To the best of our knowledge, the algorithms presented here are the first handling weighted XSAT optimization versions in non-trivial worst case time. We also investigate the corresponding weighted counting problems, namely we show that the number of all minimum, resp. maximum, weight exact satisfiability solutions of an arbitrarily weighted formula can be determined in O(n^2cdot |C|+2^{0.40567n}) time. In recent years only the unweighted counterparts of these problems have been studied cite{dahl,dahl2,porschen}.Stefan PorschenPorschen, Stefan2007-04-19T00:00:00Z2011-12-19T09:45:28Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/537This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5372007-04-19T00:00:00ZClause Set Structures and Polynomial-Time SAT-Decidable ClassesProposing a fibre view on propositional clause sets, we investigate satisfiability testing for several CNF subclasses. Specifically, we show how to decide SAT in polynomial time for formulas where each pair of different clauses intersect either in all or in one variable.Stefan PorschenPorschen, StefanEwald SpeckenmeyerSpeckenmeyer, Ewald2007-04-17T00:00:00Z2012-01-12T10:05:23Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/520This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5202007-04-17T00:00:00ZLinear CNF formulas and satisfiabilityIn this paper, we study {em linear} CNF formulas generalizing linear hypergraphs under combinatorial and complexity theoretical aspects w.r.t. SAT. We establish NP-completeness of SAT for the unrestricted linear formula class, and we show the equivalence of NP-completeness of restricted uniform linear formula classes w.r.t. SAT and the existence of unsatisfiable uniform linear witness formulas. On that basis we prove the NP-completeness of SAT for the uniform linear classes in a proof-theoretic manner by constructing however large-sized formulas. Interested in small witness formulas, we exhibit some combinatorial features of linear hypergraphs closely related to latin squares and finite projective planes helping to construct somehow dense, and significantly smaller unsatisfiable k -uniform linear formulas, at least for the cases k=3,4 .Stefan PorschenPorschen, StefanEwald SpeckenmeyerSpeckenmeyer, EwaldXishun ZhaoZhao, Xishun2007-04-12T00:00:00Z2011-10-27T11:54:50Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/499This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/4992007-04-12T00:00:00ZSatisfiability of Mixed Horn FormulasIn this paper the class of {em mixed Horn formulas} is introduced that contain a Horn part and a 2-CNF (also called quadratic) part. We show that SAT remains NP-complete for such instances and also that any CNF formula can be encoded in terms of a mixed Horn formula in polynomial time. Further, we provide an exact deterministic algorithm showing that SAT for mixed Horn formulas containing n variables is solvable in time O(2^{0.5284n}). A strong argument showing that it is hard to improve a time bound of O(2^{n/2}) for mixed Horn formulas is provided. We also obtain a fixed-parameter tractability classification for SAT restricted to mixed Horn formulas C of at most k variables in its positive 2-CNF part providing the bound O(|C|2^{0.5284k}) . We further show that the NP-hard optimization problem minimum weight SAT for mixed Horn formulas can be solved in time O(2^{0.5284n}) if non-negative weights are assigned to the variables. Motivating examples for mixed Horn formulas are level graph formulas [B. Randerath, E. Speckenmeyer, E. Boros, P. Hammer, A. Kogan, K. Makino, B. Simeone, O. Cepek, A satisfiability formulation of problems on level graphs, ENDM 9 (2001)] and graph colorability formulas.Stefan PorschenPorschen, StefanEwald SpeckenmeyerSpeckenmeyer, Ewald2007-04-05T00:00:00Z2011-08-15T12:45:36Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/461This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/4612007-04-05T00:00:00ZOn Generalizations of the Shadow Independent Set ProblemThe {em shadow independent set problem (SIS)} being a new NP-complete problem in algorithmic graph theory was introduced in cite{Franco}. It considers a forest F of kin IN (rooted) trees and nin IN vertices. Further a function sigma is given mapping the set of all leaves into the set of all vertices of F . Defining the {em shadow} of a leaf ell as the subtree rooted at sigma(ell) SIS asks for the existence of a set S of leaves exactly one from each tree, such that no leaf of S is contained in the shadow of any leaf in S . In cite{Franco} the {em fixed parameter tractability (FPT)} of SIS has been shown by obtaining O(n^2k^k) as an upper bound for its computational complexity. Recently, a new FPT bound O(n^33^k) for SIS was obtained in cite{Porschen} by dynamic programming techniques. In the present paper FPT is investigated for several generalizations of SIS. First sigma is replaced by a binary relation Sigma assigning an arbitrary number r(ell)in IN of pointers to each leaf ell . Substituting F by a set of directed acyclic graphs yields a second (structural) generalization. We are able to obtain FPT bounds for these problems generalizing the techniques in cite{Porschen}, which cannot be achieved adapting the results in cite{Franco}.Stefan PorschenPorschen, Stefan2007-02-01T00:00:00Z2011-12-19T09:44:53Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/534This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5342007-02-01T00:00:00ZAlgorithms for Variable-Weighted 2-SAT and Dual ProblemsIn this paper we study NP-hard weighted satisfiability optimization problems for the class 2-CNF providing worst-case upper time bounds. Moreover we consider the monotone dual class consisting of clause sets where all variables occur at most twice. We show that weighted SAT, XSAT and NAESAT optimization problems for this class are polynomial time solvable using appropriate reductions to specific polynomial time solvable graph problems.Stefan PorschenPorschen, StefanEwald SpeckenmeyerSpeckenmeyer, Ewald2007-01-30T00:00:00Z2011-12-19T09:44:57Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/532This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5322007-01-30T00:00:00ZClause set structures and satisfiabilityWe propose a new perspective on propositional clause sets and on that basis we investigate (new) polynomial time SAT-testable classes. Moreover, we study autarkies using a closure concept. A specific simple type of closures the free closures leads to a further formula class called hyperjoins that is studied w.r.t. SAT.Stefan PorschenPorschen, StefanEwald SpeckenmeyerSpeckenmeyer, Ewald2005-11-23T00:00:00Z2011-12-19T09:45:23Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/501This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5012005-11-23T00:00:00ZA new parameterization of the shadow problemThe shadow problem (SIS) gets as input a forest F , and a map that assigns subtrees, called shadows, to leaves of F . SIS asks whether there exists a set of |F| leaves, one from each tree, such that no leaf lies in the shadow of another. Usually SIS is considered as a parameterized problem with parameter k bounding the cardinality of F , for which some fixed-parameter tractability time bounds have been proven. In this paper, we propose a different parameterization of SIS using two independent parameters, namely k as above, and s bounding the shadow size. We provide a kernelization w.r.t. the new parameterization, and prove a fixed-parameter tractability bound of O(kcdot n^2+p(k,s)3^k) where p is a polynomial in the parameters k,s .Stefan PorschenPorschen, Stefan2005-03-01T00:00:00Z2012-01-12T10:56:58Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/476This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/4762005-03-01T00:00:00ZTabu-Sat and Walksat for Level Graph FormulasThis paper provides an empirical study of stochastic local search procedures for solving the MAXSAT problem on propositional formulas. Concretely, we first compare Walksat and (variants of) Tabu-Sat for MAX2SAT and MAX3SAT on arbitrary random CNF formulas. Second, we compare conveniently adapted versions of these procedures on level graph formulas encoding the arc crossing minimization problem for randomly generated level graphs. The Tabu-Sat procedure introduced here, dynamically modifies the tabulength parameter when a cycle in the search space is detected. Another variant called Vector-Tabu-Sat manages a tabulength parameter for every Boolean variable independently. Several numerical experiments indicate that our variants of Tabu-Sat are superior to Walksat when the number of clauses increases.Stefan PorschenPorschen, StefanEwald SpeckenmeyerSpeckenmeyer, EwaldBert RanderathRanderath, BertMattias GärtnerGärtner, Mattias