Constraint Satisfaction Problems Parameterized above or below Tight Bounds: A Survey

Gutin, Gregory; Yeo, Anders

doi:10.1007/978-3-642-30891-8_14

Cited by 19 publications

(9 citation statements)

References 63 publications

(208 reference statements)

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“…For instance, if one can prove that any solution of a given minimization problem is of cost at least B, then one can ask for a solution of cost B + c and parameterize by c. This idea, called "above guarantee parameterization" was introduced by Mahajan et al (2009) and first applied to MAX SAT and MAX CUT problems. It then became a fruitful line of research with similar results obtained for many other problems (among others, see Cygan et al (2013); Gutin et al (2007); Gutin and Yeo (2012); Mahajan et al (2009)).…”

Section: Parameterizationsmentioning

confidence: 62%

Multidimensional Binary Vector Assignment Problem: Standard, Structural and Above Guarantee Parameterizations

Bougeret

Duvillié

Giroudeau

et al. 2015

Fundamentals of Computation Theory

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In this article we focus on the parameterized complexity of the Multidimensional Binary Vector Assignment problem (called BMVA). An input of this problem is defined by m disjoint sets V 1 , V 2 , . . . , V m , each composed of n binary vectors of size p. An output is a set of n disjoint m-tuples of vectors, where each m-tuple is obtained by picking one vector from each set V i . To each m-tuple we associate a p dimensional vector by applying the bit-wise AND operation on the m vectors of the tuple. The objective is to minimize the total number of zeros in these n vectors. BMVA can be seen as a variant of multidimensional matching where hyperedges are implicitly locally encoded via labels attached to vertices, but was originally introduced in the context of integrated circuit manufacturing.We provide for this problem FPT algorithms and negative results (ET H-based results, W2-hardness and a kernel lower bound) according to several parameters: the standard parameter k (i.e. the total number of zeros), as well as two parameters above some guaranteed values.

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Section: Parameterizationsmentioning

confidence: 62%

Multidimensional Binary Vector Assignment Problem: Standard, Structural and Above Guarantee Parameterizations

Bougeret

Duvillié

Giroudeau

et al. 2015

Fundamentals of Computation Theory

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“…Kernelization can be seen as a polynomial reduction of a parameterized problem to itself. Here we present it as a special case of a more general concept of reduction called bikernel (see [60,71,72] for earlier uses of this concept).…”

Section: (Bi)kernelizationmentioning

confidence: 99%

A Retrospective on (Meta) Kernelization

Thilikos

2020

Treewidth, Kernels, and Algorithms

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In parameterized complexity, a kernelization algorithm can be seen as a reduction of a parameterized problem to itself, so that the produced equivalent instance has size depending exclusively on the parameter. If this size is polynomial, then then we say that the parameterized problem in question admits a polynomial kernelization algorithm. Kernelization can be seen as a formalization of the notion of preprocessing and has occupied a big part of the research on Multi-variate Algorithmics. The first algorithmic meta-theorem on kernelization appeared in [

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“…An alternative way to parametrize MAX SAT is to ask whether at least m + k clauses can be satisfied, where m is the expected number of satisfied constraints by a uniformly random assignment, see, e.g., [15]. As for a special case of Max SAT, it is known that the satisfiability problem of CNF formulas with n variables and cn clauses can be solved in time 2 (1−µ(c))n , where µ(c) = 1/O(log c), see [8].…”

Section: Running Timementioning

confidence: 99%