Efficient Repetitiveness Measures for Two-Dimensional Strings

This paper introduces extensions of repetitiveness measures, such as δ and γ, to two-dimensional strings. It proposes new definitions of these measures that use rectangular substrings instead of square substrings, and shows that these new measures can exhibit significant gaps compared to previous square-based definitions. The paper also generalizes straight-line programs and macro schemes to the two-dimensional setting, and analyzes the relationships between these measures.