An Algebraic Hardness Criterion for Surjective Constraint Satisfaction
Abstract
The constraint satisfaction problem (CSP) on a relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the constraints; the surjective CSP is the variant where one decides the existence of a surjective satisfying assignment onto the universe of B. We present an algebraic condition on the polymorphism clone of B and prove that it is sufficient for the hardness of the surjective CSP on a finite structure B, in the sense that this problem admits a reduction from a certain fixed-structure CSP. To our knowledge, this is the first result that allows one to use algebraic information from a relational structure B to infer information on the complexity hardness of surjective constraint satisfaction on B. A corollary of our result is that, on any finite non-trivial structure having only essentially unary polymorphisms, surjective constraint satisfaction is NP-complete.
Cite
@article{arxiv.1405.4917,
title = {An Algebraic Hardness Criterion for Surjective Constraint Satisfaction},
author = {Hubie Chen},
journal= {arXiv preprint arXiv:1405.4917},
year = {2014}
}