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Tractability and learnability arising from algebras with few subpowers
 In LICS’07
, 2007
"... A kedge operation ϕ on a finite set A is a k + 1ary operation that satisfies the identities ..."
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Cited by 54 (6 self)
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A kedge operation ϕ on a finite set A is a k + 1ary operation that satisfies the identities
The power of linear programming for valued CSPs
, 2012
"... A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. This framework includ ..."
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A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. This framework includes and generalises wellstudied constraint satisfaction problems (CSPs) and maximum constraint satisfaction problems (MaxCSPs). Our main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation. Using this result, we obtain tractability of several novel and previously widelyopen classes of VCSPs, including problems over valued constraint languages that are: (1) submodular on arbitrary lattices; (2) bisubmodular (also known as ksubmodular) on arbitrary finite domains; (3) weakly (and hence strongly) treesubmodular on arbitrary trees.
The dichotomy for conservative constraint satisfaction problems revisited
 In Proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science, LICS 2011
"... Abstract—A central open question in the study of nonuniform constraint satisfaction problems (CSPs) is the dichotomy conjecture of Feder and Vardi stating that the CSP over a fixed constraint language is either NPcomplete, or tractable. One of the main achievements in this direction is a result of ..."
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Abstract—A central open question in the study of nonuniform constraint satisfaction problems (CSPs) is the dichotomy conjecture of Feder and Vardi stating that the CSP over a fixed constraint language is either NPcomplete, or tractable. One of the main achievements in this direction is a result of Bulatov (LICS’03) confirming the dichotomy conjecture for conservative CSPs, that is, CSPs over constraint languages containing all unary relations. Unfortunately, the proof is very long and complicated, and therefore hard to understand even for a specialist. This paper provides a short and transparent proof.
Ontologybased data access: a study through disjunctive datalog, csp, and mmsnp
 IN: PODS
, 2014
"... Ontologybased data access is concerned with querying incomplete data sources in the presence of domainspecific knowledge provided by an ontology. A central notion in this setting is that of an ontologymediated query, which is a database query coupled with an ontology. In this article, we study se ..."
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Ontologybased data access is concerned with querying incomplete data sources in the presence of domainspecific knowledge provided by an ontology. A central notion in this setting is that of an ontologymediated query, which is a database query coupled with an ontology. In this article, we study several classes of ontologymediated queries, where the database queries are given as some form of conjunctive query and the ontologies are formulated in description logics or other relevant fragments of firstorder logic, such as the guarded fragment and the unary negation fragment. The contributions of the article are threefold. First, we show that popular ontologymediated query languages have the same expressive power as natural fragments of disjunctive datalog, and we study the relative succinctness of ontologymediated queries and disjunctive datalog queries. Second, we establish intimate connections between ontologymediated queries and constraint satisfaction problems (CSPs) and their logical generalization, MMSNP formulas. Third, we exploit these connections to obtain new results regarding: (i) firstorder rewritability and datalog rewritability of ontologymediated queries; (ii) P/NP dichotomies for ontologymediated queries; and (iii) the query containment problem for ontologymediated queries.
ABSORBING SUBALGEBRAS, CYCLIC TERMS, AND THE CONSTRAINT SATISFACTION PROBLEM
 LMCS VOL. 8 (1:07) 2012, PP. 1–26
, 2012
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The complexity of conservative valued CSPs
 in: Proceedings of the 23rd ACMSIAM Symposium on Discrete Algorithms (SODA'12), 2012
"... We study the complexity of valued constraint satisfaction problems (VCSP). A problem from VCSP is characterised by a constraint language, a fixed set of cost functions over a finite domain. An instance of the problem is specified by a sum of cost functions from the language and the goal is to minimi ..."
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We study the complexity of valued constraint satisfaction problems (VCSP). A problem from VCSP is characterised by a constraint language, a fixed set of cost functions over a finite domain. An instance of the problem is specified by a sum of cost functions from the language and the goal is to minimise the sum. Under the unique games conjecture, the approximability of finitevalued VCSPs is wellunderstood, see Raghavendra [FOCS’08]. However, there is no characterisation of finitevalued VCSPs, let alone generalvalued VCSPs, that can be solved exactly in polynomial time, thus giving insights from a combinatorial optimisation perspective. We consider the case of languages containing all possible unary cost functions. In the case of languages consisting of only f0;1gvalued cost functions (i.e. relations), such languages have been called conservative and studied by Bulatov [LICS’03] and
Quantified equality constraints
 In Proceedings of LICS’07
, 2007
"... An equality template (also equality constraint language) is a relational structure with infinite universe whose relations can be defined by boolean combinations of equalities. We prove a complete complexity classification for quantified constraint satisfaction problems (QCSPs) over equality template ..."
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An equality template (also equality constraint language) is a relational structure with infinite universe whose relations can be defined by boolean combinations of equalities. We prove a complete complexity classification for quantified constraint satisfaction problems (QCSPs) over equality templates: these problems are in L (decidable in logarithmic space), NPcomplete, or PSPACEcomplete. To establish our classification theorem we combine methods from universal algebra with concepts from model theory. 1
The complexity of finitevalued CSPs
 Institute of Informatics, University of Warsaw, Poland
, 2013
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The Dichotomy of List Homomorphisms for Digraphs
"... The DichotomyConjecture for Constraint Satisfaction Problems has been verified for conservative problems (or, equivalently, for list homomorphism problems) by Andrei Bulatov. An earlier case of this dichotomy, for list homomorphisms to undirected graphs, came with an elegant structural distinction b ..."
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The DichotomyConjecture for Constraint Satisfaction Problems has been verified for conservative problems (or, equivalently, for list homomorphism problems) by Andrei Bulatov. An earlier case of this dichotomy, for list homomorphisms to undirected graphs, came with an elegant structural distinction between the tractable and intractable cases. Such structural characterization is absent in Bulatov’s classification, and Bulatov asked whether one can be found. We provide an answer in the case of digraphs. In the process we give forbidden structure characterizations of the existence of certain polymorphisms relevant in Bulatov’s dichotomy classification. The key concept we introduce is that of a digraph asteroidal triple (DAT). The dichotomy then takes the following form. If a digraph H has a DAT, then the list homomorphism