  This paper presents a technique for symmetry reduction that adaptively
assigns a prefix of variables in a system of constraints so that the generated
prefix-assignments are pairwise nonisomorphic under the action of the symmetry
group of the system. The technique is based on McKay's canonical extension
framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the
technique are (i) adaptability---the prefix sequence can be user-prescribed and
truncated for compatibility with the group of symmetries; (ii)
parallelizability---prefix-assignments can be processed in parallel
independently of each other; (iii) versatility---the method is applicable
whenever the group of symmetries can be concisely represented as the
automorphism group of a vertex-colored graph; and (iv) implementability---the
method can be implemented relying on a canonical labeling map for
vertex-colored graphs as the only nontrivial subroutine. To demonstrate the
practical applicability of our technique, we have prepared an experimental
open-source implementation of the technique and carry out a set of experiments
that demonstrate ability to reduce symmetry on hard instances. Furthermore, we
demonstrate that the implementation effectively parallelizes to compute
clusters with multiple nodes via a message-passing interface.
