Network Satisfaction for Symmetric Relation Algebras with a Flexible Atom

Bodirsky, Manuel; Knäuer, Simon

doi:10.1609/aaai.v35i7.16773

Cited by 4 publications

(4 citation statements)

References 37 publications

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“…Moreover, Hirsch (1996) proposed studying the computational complexity of CSPs for relation algebras, with obvious applications in AI. Inspired by this research programme, Bodirsky and Knäuer (2021) recently identified sufficient conditions for homogeneity of relation algebras. Their results provide further examples of CSPs that are covered by Theorem 5.…”

Section: Examplesmentioning

confidence: 99%

Solving Infinite-Domain CSPs Using the Patchwork Property

Dabrowski¹,

Jönsson²,

Ordyniak³

et al. 2021

AAAI

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The constraint satisfaction problem (CSP) has important applications in computer science and AI. In particular, infinite-domain CSPs have been intensively used in subareas of AI such as spatio-temporal reasoning. Since constraint satisfaction is a computationally hard problem, much work has been devoted to identifying restricted problems that are efficiently solvable. One way of doing this is to restrict the interactions of variables and constraints, and a highly successful approach is to bound the treewidth of the underlying primal graph. Bodirsky & Dalmau [J. Comput. System. Sci., 79(1), 2013] and Huang et al. [Artif. Intell., 195, 2013] proved that CSP(Γ) can be solved in n^(f(w)) time (where n is the size of the instance, w is the treewidth of the primal graph and f is a computable function) for certain classes of constraint languages Γ. We improve this bound to f(w)n^(O(1)), where the function f only depends on the language Γ, for CSPs whose basic relations have the patchwork property. Hence, such problems are fixed-parameter tractable and our algorithm is asymptotically faster than the previous ones. Additionally, our approach is not restricted to binary constraints, so it is applicable to a strictly larger class of problems than that of Huang et al. However, there exist natural problems that are covered by Bodirsky & Dalmau's algorithm but not by ours.

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Section: Examplesmentioning

confidence: 99%

Solving Infinite-Domain CSPs Using the Patchwork Property

Dabrowski¹,

Jönsson²,

Ordyniak³

et al. 2021

AAAI

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“…On the other hand, many computational problems, even as simple as the digraph acyclicity problem, can be formulated as CSPs only with an infinite template. Infinite-domain CSPs also play an important role in several branches of computer science, e.g., they are used for the study of finite-domain promise CSPs [2] and they find applications in artificial intelligence [12,13,10,17,7,18,19].…”

Section: Introductionmentioning

confidence: 99%

“…Conjecture 1 has been confirmed for many subclasses: for example for CSPs of all structures first-order definable in finitely bounded homogeneous graphs [24,20], in (Q, <) [16], in any unary structure [22], in the random poset [34], in the random tournament [38], or in the homogeneous branching C-relation [14], as well as for all CSPs in the class MMSNP [19], for CSPs of representations of some relational algebras [17] and for CSPs of ω-categorical monadically stable structures [28].…”

Section: Introductionmentioning

confidence: 99%

An order out of nowhere: a new algorithm for infinite-domain CSPs

Mottet¹,

Pinsker²,

Nagy³

2023

Preprint

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We consider constraint satisfaction problems whose relations are defined in first-order logic over any uniform hypergraph satisfying certain weak abstract structural conditions. Our main result is a P/NP-complete complexity dichotomy for such CSPs. Surprisingly, the large class of structures under consideration falls into a mixed regime where neither the classical complexity reduction to finite-domain CSPs can be used as a black box, nor does the class exhibit order properties, known to prevent the application of this reduction. We introduce an algorithmic technique inspired by classical notions from the theory of finite-domain CSPs, and prove its correctness based on symmetries that depend on a linear order that is external to the structures under consideration.

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“…This article is the full version of results described in a conference article (Bodirsky & Knäuer, 2021).…”

Section: Introductionmentioning

confidence: 99%

The Complexity of Network Satisfaction Problems for Symmetric Relation Algebras with a Flexible Atom

Bodirsky¹,

Knäuer

2022

jair

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Robin Hirsch posed in 1996 the Really Big Complexity Problem: classify the computational complexity of the network satisfaction problem for all finite relation algebras A. We provide a complete classification for the case that A is symmetric and has a fexible atom; in this case, the problem is NP-complete or in P. The classification task can be reduced to the case where A is integral. If a finite integral relation algebra has a flexible atom, then it has a normal representation B. We can then study the computational complexity of the network satisfaction problem of A using the universal-algebraic approach, via an analysis of the polymorphisms of B. We also use a Ramsey-type result of Nešetřil and Rödl and a complexity dichotomy result of Bulatov for conservative finite-domain constraint satisfaction problems.

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Network Satisfaction for Symmetric Relation Algebras with a Flexible Atom

Cited by 4 publications

References 37 publications

Solving Infinite-Domain CSPs Using the Patchwork Property

Solving Infinite-Domain CSPs Using the Patchwork Property

An order out of nowhere: a new algorithm for infinite-domain CSPs

The Complexity of Network Satisfaction Problems for Symmetric Relation Algebras with a Flexible Atom

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