https://hal.inria.fr/inria-00455989Takhanov, RustemRustemTakhanovDepartment of Computer and Information Science - Linköping University - LIU - Linköping UniversityDichotomy theorem for general Minimum Cost Homomorphisms ProblemHAL CCSD2010minimum cost homomorphisms problemrelational clonesconstraint satisfaction problemperfect graphssupervised learning[INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG][INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC]Loria, PublicationsJean-Yves Marion and Thomas Schwentick2010-02-11 15:00:302010-02-11 21:54:422010-02-11 21:54:42enConference papersapplication/pdf1In the classical Constraint Satisfaction Problem(CSP) two finite models are given and we are asked to find their homomorphism. In the MinHom problem, besides the models, a set of weighted pairs of elements of this two models is given and the task is to find a homomorphism that maximizes the weight of pairs consistent with the homomorphism, i.e. pairs for which homomorphism maps the first element of the pair to the second element. MinHom can be considered as a generic model for a class of combinatorial optimization problems, one of which is a maximal independent set. It appears naturally in defence logistic and supervised learning. This problem shares a lot of common with the classical CSP. We show that it allows similar algebraic approach to the classification of tractable cases of this problem that connects it with relational and functional clones of multi-valued logic. Using this approach we obtain complete classification of polynomially tractable subcases of MinHom. As a result of this classification we confirm general dichotomy conjecture that was given for various special cases of MinHom in terms of digraph theory[12,11].