Approximation Properties of NP Minimization Classes

Kolaitis, Phokion G.; Thakur, M.N.

doi:10.1006/jcss.1995.1031

Cited by 52 publications

(23 citation statements)

References 14 publications

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“…The class MIN F + Π 1 was introduced by Kolaitis and Thakur in a framework of syntactically defined classes of optimization problems [26]. In a follow-up paper they showed that every problem in MIN F + Π 1 is constant-factor approximable [27]. We will prove that the standard parameterization of any problem in MIN F + Π 1 admits a polynomial kernelization.…”

Section: Hypergraphs and Sunflowersmentioning

confidence: 88%

“…Its superclass MAX NP also contains Max Sat amongst others. Kolaitis and Thakur generalized the approach of examining the logical definability of optimization problems and defined further classes of minimization and maximization problems [26,27]. Amongst others they introduced the class MIN F + Π 1 of problems whose optimum can be expressed as the minimum weight of an assignment (i.e., number of ones) that satisfies a certain universal first-order formula.…”

Section: Kernel Sizementioning

confidence: 99%

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Polynomial Kernelizations for MIN F+Π1 and MAX NP

Kratsch

2011

Algorithmica

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It has been observed in many places that constant-factor approximable problems often admit polynomial or even linear problem kernels for their decision versions, e.g., VERTEX COVER, FEEDBACK VERTEX SET, and TRIANGLE PACK-ING. While there exist examples like BIN PACKING, which does not admit any kernel unless P = NP, there apparently is a strong relation between these two polynomialtime techniques. We add to this picture by showing that the natural decision versions of all problems in two prominent classes of constant-factor approximable problems, namely MIN F + 1 and MAX NP, admit polynomial problem kernels. Problems in MAX SNP, a subclass of MAX NP, are shown to admit kernels with a linear base set, e.g., the set of vertices of a graph. This extends results of Cai and Chen (J. Comput. Syst. Sci. 54(3): 465-474, 1997), stating that the standard parameterizations of problems in MAX SNP and MIN F + 1 are fixed-parameter tractable, and complements recent research on problems that do not admit polynomial kernelizations (Bodlaender et al. in J. Comput. Syst. Sci. 75(8): 423-434, 2009).

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Section: Hypergraphs and Sunflowersmentioning

confidence: 88%

Section: Kernel Sizementioning

confidence: 99%

Polynomial Kernelizations for MIN F+Π1 and MAX NP

Kratsch

2011

Algorithmica

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“…For instance, maximization problems defined by constraint free NP Datalog queries where negation is only applied to guess atoms or atoms not depending on guess atoms (called deterministic) are constant approximable (Greco and Saccà 1997). Indeed, these problems belong to the class of constant approximable optimization problems MAX Σ 1 3 (Kolaitis and Thakur 1995) and, therefore, NP Datalog could also be used to define the class of approximable optimization problems, but this is outside the scope of this paper.…”

Section: Definitionmentioning

confidence: 99%

atalog: A logic language for expressing search and optimization problems

Greco

Molinaro

Trubitsyna

et al. 2010

Theory and Practice of Logic Programming

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This paper presents a logic language for expressing NP search and optimization problems. Specifically, first a language obtained by extending (positive) DATALOG with intuitive and efficient constructs (namely, stratified negation, constraints, and exclusive disjunction) is introduced. Next, a further restricted language only using a restricted form of disjunction to define (nondeterministically) subsets (or partitions) of relations is investigated. This language, called NP Datalog, captures the power of DATALOG ¬ in expressing search and optimization problems. A system prototype implementing NP Datalog is presented. The system translates NP Datalog queries into Optimization Programming Language (OPL) programs which are executed by the ILOG OPL Development Studio. Our proposal combines easy formulation of problems, expressed by means of a declarative logic language, with the efficiency of the ILOG System. Several experiments show the effectiveness of this approach.

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“…[Sketch] The proof is based on the logical characterization of optimization problems [16,181, the technique of Papadimitriou and Yannakakis [19], and the techniques we developed in Section 3. I In fact, one can show that the converse of Lemma 5.2 is also true, i.e.…”

Section: Definitionmentioning

confidence: 99%

On fixed-parameter tractability and approximability of NP-hard optimization problems

Cai

Chen

[1993] the 2nd Israel Symposium on Theory and Computing Systems

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Fixed-pammeter tractability and approximabilityof NP-hard optimization problems are studied based on a model GC(s(n),IIt). Our main results are (1) a class of NP-hard optimization problems, including Dominating-Set and Zero-One Integer-Progmm m ing, a re jixed-pam me te r tractable if and only if GC(s(n),IIk) C P for some s(n) E w(1ogn); (2) Most approximable NP-hard optimization problems are jixedparameter tmctable. In particular, the class MAX N P is jixed-parameter tmctable; (8) a class of optimization problems do not have fully polynomial time approximation scheme unless GC(s(n), T I : ) C P for some s(n) E o(1ogn) and for some k > 1; and (4) every jixed-parameter tmctable optimization problem can be approximated in polynomial time to a non-trivial ratio. 0-8186-3630-0193 $3.00 0 1993 IEEE

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Approximation Properties of NP Minimization Classes

Cited by 52 publications

References 14 publications

Polynomial Kernelizations for MIN F+Π1 and MAX NP

Polynomial Kernelizations for MIN F+Π1 and MAX NP

atalog: A logic language for expressing search and optimization problems

On fixed-parameter tractability and approximability of NP-hard optimization problems

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