  We introduce two algorithms, RECURSIA and RRT, designed to increase the
compression factor achievable using point-set cover algorithms based on the SIA
and SIATEC pattern discovery algorithms. SIA computes the maximal translatable
patterns (MTPs) in a point set, while SIATEC computes the translational
equivalence class (TEC) of every MTP in a point set, where the TEC of an MTP is
the set of translationally invariant occurrences of that MTP in the point set.
In its output, SIATEC encodes each MTP TEC as a pair, <P,V>, where P is the
first occurrence of the MTP and V is the set of non-zero vectors that map P
onto its other occurrences. RECURSIA recursively applies a TEC cover algorithm
to the pattern P, in each TEC, <P,V>, that it discovers. RRT attempts to remove
translators from V in each TEC without reducing the total set of points covered
by the TEC. When evaluated with COSIATEC, SIATECCompress and Forth's algorithm
on the JKU Patterns Development Database, using RECURSIA with or without RRT
increased compression factor and recall but reduced precision. Using RRT alone
increased compression factor and reduced recall and precision, but had a
smaller effect than RECURSIA.
