Computational Complexity of the Minimum Cost Homomorphism Problem on Three-Element Domains

نویسنده

  • Hannes Uppman
چکیده

In this paper we study the computational complexity of the (extended) minimum cost homomorphism problem (Min-Cost-Hom) as a function of a constraint language, i.e. a set of constraint relations and cost functions that are allowed to appear in instances. A wide range of natural combinatorial optimisation problems can be expressed as Min-Cost-Homs and a classification of their complexity would be highly desirable, both from a direct, applied point of view as well as from a theoretical perspective. Min-Cost-Hom can be understood either as a flexible optimisation version of the constraint satisfaction problem (CSP) or a restriction of the (general-valued) valued constraint satisfaction problem (VCSP). Other optimisation versions of CSPs such as the minimum solution problem (Min-Sol) and the minimum ones problem (Min-Ones) are special cases of Min-Cost-Hom. The study of VCSPs has recently seen remarkable progress. A complete classification for the complexity of finite-valued languages on arbitrary finite domains has been obtained Thapper and Živný [STOC’13]. However, understanding the complexity of languages that are not finite-valued appears to be more difficult. Min-Cost-Hom allows us to study problematic languages of this type without having to deal with with the full generality of the VCSP. A recent classification for the complexity of three-element Min-Sol, Uppman [ICALP’13], takes a step in this direction. In this paper we extend this result considerably by determining the complexity of three-element Min-Cost-Hom.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Computational Complexity of the Extended Minimum Cost Homomorphism Problem on Three-Element Domains

In this paper we study the computational complexity of the extended minimum cost homomorphism problem (Min-Cost-Hom) as a function of a constraint language, i.e. a set of constraint relations and cost functions that are allowed to appear in instances. A wide range of natural combinatorial optimisation problems can be expressed as extended Min-Cost-Homs and a classification of their complexity w...

متن کامل

Bounded Tree-Width and CSP-Related Problems

We study the complexity of structurally restricted homomorphism and constraint satisfaction problems. For every class of relational structures C, let LHOM(C, _) be the problem of deciding whether a structure A ∈ C has a homomorphism to a given arbitrary structure B, when each element in A is only allowed a certain subset of elements of B as its image. We prove, under a certain complexity-theore...

متن کامل

Minimum Cost and List Homomorphisms to Semicomplete Digraphs

For digraphs D and H, a mapping f : V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). Let H be a fixed directed or undirected graph. The homomorphism problem for H asks whether a directed or undirected graph input digraph D admits a homomorphism to H. The list homomorphism problem for H is a generalization of the homomorphism problem for H, where every vertex x ∈ V (...

متن کامل

Minimum Cost Homomorphisms of Digraphs

For digraphs D and H , a mapping f : V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). For a fixed directed or undirected graph H and an input graph D, the problem of verifying whether there exists a homomorphism of D to H has been studied in a large number of papers. We study an optimization version of this decision problem. Our optimization problem is motivated by ...

متن کامل

OPTIMUM DESIGN OF FILAMENT–WOUND LAMINATED CONICAL SHELLS FOR BUCKLING USING THE PENALTY FUNCTION

Optimum laminate configuration for minimum weight of filament–wound laminated conical shells subject to buckling load constraint is investigated. In the case of a laminated conical shell the thickness and the ply orientation (the design variables) are functions of the shell coordinates, influencing both the buckling load and its weight. These effects complicate the optimization problem consider...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • CoRR

دوره abs/1308.1394  شماره 

صفحات  -

تاریخ انتشار 2013