  We study approximability of regular constraint satisfaction problems, i.e.,
CSPs where each variable in an instance has the same number of occurrences. In
particular, we show that for any CSP $\Lambda$, existence of an $\alpha$
approximation algorithm for unweighted regular Max-CSP $\Lambda$ implies
existence of an $\alpha-o(1)$ approximation algorithm for weighted Max-CSP
$\Lambda$ in which regularity of the instances is not imposed. We also give an
analogous result for Min-CSPs, and therefore show that up to arbitrarily small
error it is sufficient to conduct the study of approximability of CSPs only on
regular unweighted instances.
