On the complexity of MMSNP

Manuel Bodirsky (1) , Hubert Chen (2) , Tomas Feder (3)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 Computer Science Department [San Sebastian]
3 Computer Science Department [Stanford]

Monotone monadic strict NP (MMSNP) is a class of computational problems that is closely related to the class of constraint satisfaction problems for constraint languages over finite domains. It is known that one of those classes has a complexity dichotomy if and only if the other class has. Whereas the dichotomy conjecture has been verified for several subclasses of constraint satisfaction problems, little is known about the the computational complexity for subclasses of MMSNP. In this paper we completely classify the complexity of MMSNP for the case where the obstructions are monochromatic and where loops in the input are forbidden. That is, we determine the computational complexity of natural partition problems of the following type. For fixed sets of finite structures S_1, ..., S_k, decide whether a given loopless structure can be vertex-partitioned into k parts such that for each i <= k none of the structures in S_i is homomorphic to the i-th part.

Domaines: Complexité [cs.CC]

Manuel Bodirsky, Hubert Chen, Tomas Feder. On the complexity of MMSNP. SIAM Journal on Discrete Mathematics, 2012, 26 (1), pp.404-414. ⟨hal-00756920⟩