We extend the concept of deterministic sampling to the two-dimensional
pattern matching problem. We show that almost all patterns have a log
arithmic deterministic sample. There are 2D-matching algorithms which
work efficiently for almost all patterns. They solve the 2D-matching p
roblem in linear sequential time with O(1) space, or, alternatively in
O(1) parallel time with linear number of processors. This is the firs
t attempt to reduce the space for two-dimensional pattern matching.