Lars Engebretsen

We show that the k-CSP problem over a finite Abelian group G

cannot be approximated within |G|^{k-O(sqrt{k})}-epsilon, for

any constant epsilon>0, unless P=NP. This lower bound matches

well with the best known upper bound, |G|^{k-1}, of Serna,

Trevisan and Xhafa. The proof uses a combination of PCP

techniques---most notably a ...
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Víctor Dalmau

We give in this paper a different and simpler proof of the tractability of Mal'tsev contraints.

more >>>Serge Gaspers, Stefan Szeider

We investigate the parameterized complexity of deciding whether a constraint network is $k$-consistent. We show that, parameterized by $k$, the problem is complete for the complexity class co-W[2]. As secondary parameters we consider the maximum domain size $d$ and the maximum number $\ell$ of constraints in which a variable occurs. ... more >>>

Jason Li, Ryan O'Donnell

We show that the basic semidefinite programming relaxation value of any constraint satisfaction problem can be computed in NC; that is, in parallel polylogarithmic time and polynomial work. As a complexity-theoretic consequence we get that MIP1$[k,c,s] \subseteq $ PSPACE provided $s/c \leq (.62-o(1))k/2^k$, resolving a question of Austrin, Håstad, and ... more >>>