In this paper we give an algorithm for streaming k-edit approximate pattern matching which uses space Õ(k²) and time Õ(k²) per arriving symbol. This improves substantially on the recent algorithm of Kociumaka, Porat and Starikovskaya [Kociumaka et al., 2022] which uses space Õ(k⁵) and time Õ(k⁸) per arriving symbol. In the k-edit approximate pattern matching problem we get a pattern P and text T and we want to identify all substrings of the text T that are at edit distance at most k from P. In the streaming version of this problem both the pattern and the text arrive in a streaming fashion symbol by symbol and after each symbol of the text we need to report whether there is a current suffix of the text with edit distance at most k from P. We measure the total space needed by the algorithm and time needed per arriving symbol.
@InProceedings{bhattacharya_et_al:LIPIcs.ICALP.2023.22, author = {Bhattacharya, Sudatta and Kouck\'{y}, Michal}, title = {{Streaming k-Edit Approximate Pattern Matching via String Decomposition}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {22:1--22:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.22}, URN = {urn:nbn:de:0030-drops-180741}, doi = {10.4230/LIPIcs.ICALP.2023.22}, annote = {Keywords: Approximate pattern matching, edit distance, streaming algorithms} }
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