  We extend the notion of a strong backdoor from the CSP setting to the Valued
CSP setting (VCSP, for short). This provides a means for augmenting a class of
tractable VCSP instances to instances that are outside the class but of small
distance to the class, where the distance is measured in terms of the size of a
smallest backdoor. We establish that VCSP is fixed-parameter tractable when
parameterized by the size of a smallest backdoor into every tractable class of
VCSP instances characterized by a (possibly infinite) tractable valued
constraint language of finite arity and finite domain. We further extend this
fixed-parameter tractability result to so-called "scattered classes" of VCSP
instances where each connected component may belong to a different tractable
class.
