Conservative constraint satisfaction re-revisited

Conservative constraint satisfaction problems (CSPs) constitute an important particular case of the general CSP, in which the allowed values of each variable can be restricted in an arbitrary way. Problems of this type are well studied for graph homomorphisms. A dichotomy theorem characterizing conservative CSPs solvable in polynomial time and proving that the remaining ones are NP-complete was proved by Bulatov in 2003. Its proof, however, is quite long and technical. A shorter proof of this result based on the absorbing subuniverses technique was suggested by Barto in 2011. In this paper we give a short elementary prove of the dichotomy theorem for the conservative CSP

Algebraic Properties of Valued Constraint Satisfaction Problem

The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP 2005]. We introduce the notions of weighted algebras and varieties and use the Galois connection due to Cohen et al. [SICOMP 2013] to link VCSP languages to weighted algebras. We show that the difficulty of VCSP depends only on the weighted variety generated by the associated weighted algebra. Paralleling the results for CSPs we exhibit a reduction to cores and rigid cores which allows us to focus on idempotent weighted varieties. Further, we propose an analogue of the Algebraic CSP Dichotomy Conjecture; prove the hardness direction and verify that it agrees with known results for VCSPs on two-element sets [Cohen et al. 2006], finite-valued VCSPs [Thapper and Zivny 2013] and conservative VCSPs [Kolmogorov and Zivny 2013].Comment: arXiv admin note: text overlap with arXiv:1207.6692 by other author

Elastic consequences of a single plastic event : a step towards the microscopic modeling of the flow of yield stress fluids

With the eventual aim of describing flowing elasto-plastic materials, we focus on the elementary brick of such a flow, a plastic event, and compute the long-range perturbation it elastically induces in a medium submitted to a global shear strain. We characterize the effect of a nearby wall on this perturbation, and quantify the importance of finite size effects. Although for the sake of simplicity most of our explicit formulae deal with a 2D situation, our statements hold for 3D situations as well.Comment: submitted to EPJ