Dichotomies for classes of homomorphism problems involving unary functions
Theoretical Computer Science
A polynomial-time algorithm for near-unanimity graphs
Journal of Algorithms
Graphs, polymorphisms and the complexity of homomorphism problems
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Minimum Cost Homomorphism Dichotomy for Oriented Cycles
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Dualities for Constraint Satisfaction Problems
Complexity of Constraints
Theoretical Computer Science
Minimum cost homomorphisms to reflexive digraphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Minimum cost homomorphisms to oriented cycles with some loops
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
The dichotomy of list homomorphisms for digraphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
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We show that, for every choice of an oriented cycle H, the problem of whether an input digraph G has a homomorphism to H is either polynomially solvable or NP-complete. Along the way, we obtain simpler proofs for two known polynomial cases, namely, oriented paths and unbalanced oriented cycles, and exhibit two new simple polynomial cases of balanced oriented cycles. The more difficult cases of the classification are handled by means of a new problem, the bipartite boolean satisfiability problem. In general, the k-partite boolean satisfiability problems are shown to be either polynomially solvable or NP-complete, thus generalizing Schaefer's classification of boolean satisfiability problems.