  Zimin words are very special finite words which are closely related to the
pattern-avoidability problem. This problem consists in testing if an instance
of a given pattern with variables occurs in almost all words over any finite
alphabet. The problem is not well understood, no polynomial time algorithm is
known and its NP-hardness is also not known. The pattern-avoidability problem
is equivalent to searching for a pattern (with variables) in a Zimin word. The
main difficulty is potentially exponential size of Zimin words. We use special
properties of Zimin words, especially that they are highly compressible, to
design efficient algorithms for special version of the pattern-matching, called
here ranked matching. It gives a new interpretation of Zimin algorithm in
compressed setting. We discuss the structure of rankings of variables and
compressed representations of values of variables. Moreover, for a ranked
matching we present efficient algorithms to find the shortest instance and the
number of valuations of instances of the pattern.
