  In this paper, we investigate the hybrid tractability of binary Quantified
Constraint Satisfaction Problems (QCSPs). First, a basic tractable class of
binary QCSPs is identified by using the broken-triangle property. In this
class, the variable ordering for the broken-triangle property must be same as
that in the prefix of the QCSP. Second, we break this restriction to allow that
existentially quantified variables can be shifted within or out of their
blocks, and thus identify some novel tractable classes by introducing the
broken-angle property. Finally, we identify a more generalized tractable class,
i.e., the min-of-max extendable class for QCSPs.
