Generalized Satisfiability with Limited Occurrences per Variable: A Study through Delta-Matroid Parity

Dalmau, Víctor; Ford, Daniel K.

doi:10.1007/978-3-540-45138-9_30

Cited by 29 publications

(42 citation statements)

References 11 publications

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“…By now there is strong supporting evidence for the conjecture -in the intervening years it has been verified in many cases [11,12,13,23,24,14,38,40,51,53,54,55,60,61,62,63,67,72,136,140,171], cf. [52,106], prominently including CSP(H) for structures H with up to three vertices [25], extending the Boolean Dichotomy of [179], and for conservative structures [23], discussed in Section 5.…”

Section: H Has a Loopmentioning

confidence: 96%

Colouring, constraint satisfaction, and complexity

Hell

Nešetřil

2008

Computer Science Review

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Constraint satisfaction problems have enjoyed much attention since the early seventies, and in the last decade have become also a focus of attention amongst theoreticians. Graph colourings are a special class of constraint satisfaction problems; they offer a microcosm of many of the considerations that occur in constraint satisfaction. From the point of view of theory, they are well known to exhibit a dichotomy of complexity -the k-colouring problem is polynomial time solvable when k ≤ 2, and NP-complete when k ≥ 3. Similar dichotomy has been proved for the class of graph homomorphism problems, which are intermediate problems between graph colouring and constraint *

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Section: H Has a Loopmentioning

confidence: 96%

Colouring, constraint satisfaction, and complexity

Hell

Nešetřil

2008

Computer Science Review

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“…A key technique in proving hardness results for #CSP and related problems is pinning [12,14,19,20,23,25]. We write R zero = {0} and R one = {1} for the two unary relations that contain only zero and one, respectively.…”

Section: Boolean Constraint Satisfaction Problemsmentioning

confidence: 99%

“…Restricting the degree of instances (the maximum number of times that each variable may appear in the scopes of constraints) is incomparable but not much is known in this case. In the non-uniform Boolean case, Dalmau and Ford have shown that, as long as Γ contains the relations R zero = {0} and R one = {1}, CSP(Γ ) for instances of degree at most three has the same complexity as the case with no degree restrictions [14]. The degree-2 case has not yet been completely classified, though it is known that degree-2 CSP(Γ ) is as hard as general CSP(Γ ) whenever Γ contains R zero and R one and some relation that is not a -matroid [14,25].…”

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confidence: 97%

The complexity of approximating bounded-degree Boolean #CSP

Dyer

Goldberg

Jalsenius

et al. 2012

Information and Computation

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The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages containing the two unary constant relations {0} and {1}. When the maximum allowed degree is large enough (at least 6) we obtain a complete classification of the complexity of this problem. It is exactly solvable in polynomial time if every relation in the constraint language is affine. It is equivalent to the problem of approximately counting independent sets in bipartite graphs if every relation can be expressed as conjunctions of {0}, {1} and binary implication. Otherwise, there is no FPRAS unless NP = RP. For lower degree bounds, additional cases arise, where the complexity is related to the complexity of approximately counting independent sets in hypergraphs.

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“…If we start with a SAT instance with the number of occurrences per variable bounded by three (also an NP-complete problem [2]), we end with (V , F ) planar (each component of (V , F ) contains at most three vertices). Thus, the PAFP is NP-complete even if both G = (V , E) and (V , F ) are planar.…”

Section: Preliminariesmentioning

confidence: 99%

On the complexity of paths avoiding forbidden pairs

Kolman¹,

Pangrác²

2009

Discrete Applied Mathematics

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a b s t r a c tGiven a graph G = (V , E), two fixed vertices s, t ∈ V and a set F of pairs of vertices (called forbidden pairs), the problem of a path avoiding forbidden pairs is to find a path from s to t that contains at most one vertex from each pair in F . The problem is known to be NP-complete in general and a few restricted versions of the problem are known to be in P. We study the complexity of the problem for directed acyclic graphs with respect to the structure of the forbidden pairs.

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Generalized Satisfiability with Limited Occurrences per Variable: A Study through Delta-Matroid Parity

Cited by 29 publications

References 11 publications

Colouring, constraint satisfaction, and complexity

Colouring, constraint satisfaction, and complexity

The complexity of approximating bounded-degree Boolean #CSP

On the complexity of paths avoiding forbidden pairs

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