Abstract
Detecting and measuring repetitiveness of strings is a problem that has been extensively studied in data compression and text indexing. When the data are structured in a non-linear way, as in two-dimensional strings, inherent redundancy offers a rich source for compression, yet systematic studies on repetitiveness measures are still lacking. In this paper, we extend to two dimensions the measures \(\delta \) and \(\gamma \), defined in terms of the submatrices of the input, as well as the measures g, \(g_{rl}\), and b, which are based on copy-paste mechanisms. We study their properties and mutual relationships, and we show that the two classes of measures become incomparable when two-dimensional inputs are considered. We also compare our measures with the 2D Block Tree data structure [Brisaboa et al., Computer J., 2024], and provide some insights for the design of effective 2D compressors.
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Notes
- 1.
Analogously to the 1D setting, the parse tree of 2D SLP is an ordered labeled tree where S is the root, and the children of a variable A are the variables in its right-hand side (possibly repeated).
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Acknowledgments
LC and GM are partially funded by the PNRR ECS00000017 Tuscany Health Ecosystem, Spoke 6, CUP I53C22000780001, funded by the NextGeneration EU programme, by the spoke “FutureHPC & BigData” of the ICSC—Centro Nazionale di Ricerca in High-Performance Computing, Big Data and Quantum Computing, funded by the NextGeneration EU programme.
GR and MS are partially funded by the MUR PRIN Project “PINC, Pangenome INformatiCs: from Theory to Applications” (Grant No. 2022YRB97K).
LC, GM, MS, and GR are partially funded by the INdAM-GNCS Project CUP E53C23001670001.
CU is partially funded by ANID-Subdirección de Capital Humano/Doctorado Nacional/2021-21210580, ANID, Chile, partially funded by Basal Funds FB0001, ANID, Chile, and partially funded by Fondecyt Grant 1-230755.
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Carfagna, L., Manzini, G., Romana, G., Sciortino, M., Urbina, C. (2025). Generalization of Repetitiveness Measures for Two-Dimensional Strings. In: Lipták, Z., Moura, E., Figueroa, K., Baeza-Yates, R. (eds) String Processing and Information Retrieval. SPIRE 2024. Lecture Notes in Computer Science, vol 14899. Springer, Cham. https://doi.org/10.1007/978-3-031-72200-4_5
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