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Dualities for constraint satisfaction problems
"... In a nutshell, a duality for a constraint satisfaction problem equates the existence of one homomorphism to the nonexistence of other homomorphisms. In this survey paper, we give an overview of logical, combinatorial, and algebraic aspects of the following forms of duality for constraint satisfact ..."
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In a nutshell, a duality for a constraint satisfaction problem equates the existence of one homomorphism to the nonexistence of other homomorphisms. In this survey paper, we give an overview of logical, combinatorial, and algebraic aspects of the following forms of duality for constraint satisfaction problems: finite duality, bounded pathwidth duality, and bounded treewidth duality.
CATERPILLAR DUALITIES AND REGULAR LANGUAGES
"... Abstract. We characterize obstruction sets in caterpillar dualities in terms of regular languages, and give a construction of the dual of a regular family of caterpillars. In particular, we prove that every monadic linear Datalog program with at most one EDB per rule defines the complement of a cont ..."
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Abstract. We characterize obstruction sets in caterpillar dualities in terms of regular languages, and give a construction of the dual of a regular family of caterpillars. In particular, we prove that every monadic linear Datalog program with at most one EDB per rule defines the complement of a contraint satisfaction problem. 1.
Duality for MinMax Orderings and Dichotomy for Min Cost Homomorphisms
"... MinMax orderings correspond to conservative lattice polymorphisms. Digraphs with MinMax orderings have polynomial time solvable minimum cost homomorphism problems. They can also be viewed as digraph analogues of proper interval graphs and bigraphs. We give a forbidden structure characterization of ..."
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MinMax orderings correspond to conservative lattice polymorphisms. Digraphs with MinMax orderings have polynomial time solvable minimum cost homomorphism problems. They can also be viewed as digraph analogues of proper interval graphs and bigraphs. We give a forbidden structure characterization of digraphs with a MinMax ordering which implies a polynomial time recognition algorithm. We also similarly characterize digraphs with an extended MinMax ordering, and we apply this characterization to prove a conjectured form of dichotomy for minimum cost homomorphism problems. 1
NEARUNANIMITY POLYMORPHISMS ON STRUCTURES WITH FINITE DUALITY
"... Abstract. We introduce a combinatorial parameter on finite relational trees, called the degree of monstrosity, which measures the smallest possible arity of a nearunanimity polymorphism on a core structure with finite duality. We also show that the core structures which admit all conservative opera ..."
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Abstract. We introduce a combinatorial parameter on finite relational trees, called the degree of monstrosity, which measures the smallest possible arity of a nearunanimity polymorphism on a core structure with finite duality. We also show that the core structures which admit all conservative operations as polymorphisms are essentially the structures with finite duality whose minimal obstructions are trees with degree of monstrosity at most one. 1.
DISTRIBUTIVE LATTICE POLYMORPHISM ON REFLEXIVE GRAPHS
"... Abstract. In this paper we give two characterisations of the class of reflexive graphs admitting distributive lattice polymorphisms and use these characterisations to attack the problem of finding a polynomial time recognition algorithm for these graphs. We provide a polynomial time recognition alg ..."
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Abstract. In this paper we give two characterisations of the class of reflexive graphs admitting distributive lattice polymorphisms and use these characterisations to attack the problem of finding a polynomial time recognition algorithm for these graphs. We provide a polynomial time recognition algorithm for Rthin reflexive graphs which admit what we call Type 2 distributive lattice polymorphisms.