  We consider discrete pairwise energy minimization problem (weighted
constraint satisfaction, max-sum labeling) and methods that identify a globally
optimal partial assignment of variables. When finding a complete optimal
assignment is intractable, determining optimal values for a part of variables
is an interesting possibility. Existing methods are based on different
sufficient conditions. We propose a new sufficient condition for partial
optimality which is: (1) verifiable in polynomial time (2) invariant to
reparametrization of the problem and permutation of labels and (3) includes
many existing sufficient conditions as special cases. We pose the problem of
finding the maximum optimal partial assignment identifiable by the new
sufficient condition. A polynomial method is proposed which is guaranteed to
assign same or larger part of variables than several existing approaches. The
core of the method is a specially constructed linear program that identifies
persistent assignments in an arbitrary multi-label setting.
