We construct the first constant time value approximation schemes (CTASs) for Metric and Quasi-Metric MAX-rCSP problems for any $r ge 2$ in a preprocessed metric model of computation, improving over the previous results of [FKKV05] proven for the general core-dense MAX-rCSP problems. They entail also the first sublinear approximation schemes for constructing approximate solutions of the above optimization problems.

We construct the first constant time value approximation schemes (CTASs) for Metric and Quasi-Metric MAX-rCSP problems for any $r \ge 2$ in a preprocessed metric model of computation, improving over the previous results of [FKKV05] proven for the general core-dense MAX-rCSP problems. They entail also the first sublinear approximation schemes for constructing approximate solutions of the above optimization problems.