What the study found
The study found an O(log n)-time algorithm for internal pattern matching queries, which ask for all exact occurrences of one fragment X within another fragment Y of the same text, when the text is represented in compressed or dynamic form. The authors say this works on balanced recompression-based run-length straight-line programs and can also be used with a dynamic strings data structure.
Why the authors say this matters
The authors say the result extends internal pattern matching to compressed and dynamic strings. They also note that their procedure does not rely on preprocessing of the underlying run-length straight-line program, which makes it directly usable with a fully persistent dynamic strings structure.
What the researchers tested
The researchers studied internal pattern matching queries on a length-n text T, where X and Y are fragments of T and |Y| < 2|X|. They designed a query algorithm for balanced recompression-based run-length straight-line programs and discussed how it applies on top of an existing compressed-text representation and a dynamic strings data structure.
What worked and what didn't
The proposed procedure achieves O(log n) query time. The abstract also states that it is applicable to the cited compressed-text representation whose size is optimal as a function of text length, alphabet size, and substring complexity, and that it can be used with fully persistent updates in logarithmic time with high probability in the dynamic setting.
What to keep in mind
The abstract does not report experimental evaluation, so only the stated theoretical result is available here. It also does not provide detailed constraints, comparisons, or failure cases beyond the applicability conditions described in the summary.
Key points
- The paper presents an O(log n)-time algorithm for internal pattern matching queries.
- The method applies to balanced recompression-based run-length straight-line programs.
- The procedure does not require preprocessing of the underlying compressed representation.
- The authors say it can be used with a dynamic strings data structure supporting fully persistent updates.
- Internal pattern matching asks for all exact occurrences of fragment X within fragment Y.
Disclosure
- Research title:
- Internal pattern matching can be queried in logarithmic time on compressed texts
- Authors:
- Anouk Duyster, Tomasz Kociumaka
- Institutions:
- Max Planck Institute for Informatics, Max Planck Institute for Informatics
- Publication date:
- 2026-02-23
- OpenAlex record:
- View
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