On the Power of k-Consistency

Atserias, Albert; Bulatov, Andreǐ A.; Dalmau, Víctor

doi:10.1007/978-3-540-73420-8_26

Cited by 47 publications

(117 citation statements)

References 15 publications

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“…In particular, the above equivalence between monotonic and non-monotonic capturing strategies turns out to be very useful, because good strategies for the robber may be easily characterized as those strategies that allow the robber to run forever. See [3], for an interesting application of the robber-and-cops game in proofs regarding the power of k-Consistency in constraint satisfaction problems.…”

Section: Definition 21 ([72])mentioning

confidence: 99%

Treewidth and Hypertree Width

Gottlob¹,

Greco²,

Scarcello³

2014

Tractability

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The chapter covers methods for identifying islands of tractability for NP-hard combinatorial problems by exploiting suitable properties of their graphical structure. Acyclic structures are considered, as well as nearly acyclic ones identified by means of so-called structural decomposition methods. In particular, the chapter focuses on the tree decomposition method, which is the most powerful decomposition method for graphs, and on the hypertree decomposition method, which is its natural counterpart for hypergraphs. These problem-decomposition methods give rise to corresponding notions of width of an instance, namely, treewidth and hypertree width. It turns out that many NP-hard problems can be solved efficiently over classes of instances of bounded treewidth or hypertree width: deciding whether a solution exists, computing a solution, and even computing an optimal solution (if some cost function over solutions is specified) are all polynomial-time tasks. Example applications include problems from artificial intelligence, databases, game theory, and combinatorial auctions.

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Section: Definition 21 ([72])mentioning

confidence: 99%

Treewidth and Hypertree Width

Gottlob¹,

Greco²,

Scarcello³

2014

Tractability

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“…* 0 1 2 3 0 0 1 2 3 1 1 1 2 1 2 2 2 2 3 3 3 1 3 3 It is straightforward to verify that this operation is commutative and conservative, and is a 2-semilattice. The graph induced by this operation has edges (0, 1), (0, 2), (0, 3), (1,2), (2,3), (3,1), as well as self-edges on each of the vertices. There is thus just one strongly connected component of size strictly greater than one, namely, the component {1, 2, 3}.…”

Section: Theorem 32 Let (B ⋆) Be a Conservative 2-semilattice Such Tmentioning

confidence: 99%

“…Checking for consistency is a primary reasoning technique for the practical solution of the CSP, and has been studied theoretically from many viewpoints [22,2,4,1,3,6,5]. The most basic and simplest form of consistency is arc consistency, which algorithmically involves performing inferences concerning the set of feasible values for each variable.…”

Section: Introductionmentioning

confidence: 99%

Arc consistency and friends

Chen

Dalmau

Grußien

2011

Journal of Logic and Computation

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A natural and established way to restrict the constraint satisfaction problem is to fix the relations that can be used to pose constraints; such a family of relations is called a constraint language. In this article, we study arc consistency, a heavily investigated inference method, and three extensions thereof from the perspective of constraint languages. We conduct a comparison of the studied methods on the basis of which constraint languages they solve, and we present new polynomial-time tractability results for singleton arc consistency, the most powerful method studied.

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“…Observing that c is the variable to which the partial instantiation α cannot be extended in both directions of the proof of Claim 2, the co-W Proof. Cesati and Di Ianni [6] showed that the following parameterized problem is in W [1] (see also [3] where W[1]-completeness is established for the single-tape version of the problem).…”

Section: Independent Setmentioning

confidence: 99%

“…If a constraint network is locally consistent, then consistent instantiations to a small number of variables can be consistently extended to an additional variable. Hence local consistency avoids certain dead-ends in the search tree, in some cases it even guarantees backtrack-free search [1,20]. The simplest and most widely used form of local consistency is arc-consistency, introduced by Mackworth [23], and later generalized to k-consistency by Freuder [19].…”

Section: Introductionmentioning

confidence: 99%

The Parameterized Complexity of Local Consistency

Gaspers

Szeider

2011

Principles and Practice of Constraint Programming – CP 2011

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We investigate the parameterized complexity of deciding whether a constraint network is kconsistent. We show that, parameterized by k, the problem is complete for the complexity class co-W [2]. As secondary parameters we consider the maximum domain size d and the maximum number of constraints in which a variable occurs. We show that parameterized by k + d, the problem drops down one complexity level and becomes co-W[1]-complete. Parameterized by k + d + the problem drops down one more level and becomes fixed-parameter tractable. We further show that the same complexity classification applies to strong k-consistency, directional k-consistency, and strong directional k-consistency.Our results establish a super-polynomial separation between input size and time complexity. Thus we strengthen the known lower bounds on time complexity of k-consistency that are based on input size.

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On the Power of k-Consistency

Cited by 47 publications

References 15 publications

Treewidth and Hypertree Width

Treewidth and Hypertree Width

Arc consistency and friends

The Parameterized Complexity of Local Consistency

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