We investigate the compression sensitivity [Akagi et al., 2023] of lex-parse [Navarro et al., 2021] for two operations: (1) single character edit and (2) modification of the alphabet ordering, and give tight upper and lower bounds for both operations (i.e., we show Θ(log n) bounds for strings of length n). For both lower bounds, we use the family of Fibonacci words. For the bounds on edit operations, our analysis makes heavy use of properties of the Lyndon factorization of Fibonacci words to characterize the structure of lex-parse.
@InProceedings{nakashima_et_al:LIPIcs.MFCS.2024.75, author = {Nakashima, Yuto and K\"{o}ppl, Dominik and Funakoshi, Mitsuru and Inenaga, Shunsuke and Bannai, Hideo}, title = {{Edit and Alphabet-Ordering Sensitivity of Lex-Parse}}, booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)}, pages = {75:1--75:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-335-5}, ISSN = {1868-8969}, year = {2024}, volume = {306}, editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.75}, URN = {urn:nbn:de:0030-drops-206314}, doi = {10.4230/LIPIcs.MFCS.2024.75}, annote = {Keywords: Compression sensitivity, Lex-parse, Fibonacci words} }
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