Optimal-Time Contextual Pattern Matching in Compressed Space

[2606.31030] Optimal-Time Contextual Pattern Matching in Compressed Space Skip to main content Search Submit Donate Log in Computer Science > Data Structures and Algorithms arXiv:2606.31030 (cs) [Submitted on 30 Jun 2026 ( v1 ), last revised 21 Aug 2026 (this version, v2)] Title: Optimal-Time Contextual Pattern Matching in Compressed Space Authors: Gonzalo Navarro , Francisco Olivares View PDF HTML (experimental) Abstract: Contextual pattern matching is the task of, given a pattern $P[1,m]$, a context length $\lambda$, and a text $T[1,n]$, find all the $occ$ distinct contexts in which $P$ occurs in $T$, the context being the $\lambda$ symbols preceding and the $\lambda$ symbols following the occurrence; a text position where each context occurs must be output. While the problem can be solved in optimal time $O(m+occ)$ using $O(n)$-space precomputed data structures on $T$, this type of search is particularly relevant on large repetitive text collections, where $O(n)$ space can be prohibitive. We present the first optimal-time solution that runs in compressed space, namely that of a symmetric CDAWG (SCDAWG) of $T$. Further, we show how the set of $occ$ solutions can be enumerated with $O(\log\log\lambda)$ delay after $O(m)$-time preprocessing of $P$. To achieve this, we develop an improved linear-space distance-sensitive weighted ancestor data structure. Subjects: Data Structures and Algorithms (cs.DS) Cite as: arXiv:2606.31030 [cs.DS] (or arXiv:2606.31030v2 [cs.DS] for this version) https://doi.org/10.48550/arXiv.2606.31030 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Francisco Olivares [ view email ] [v1] Tue, 30 Jun 2026 01:56:53 UTC (37 KB) [v2] Fri, 21 Aug 2026 20:50:50 UTC (38 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.DS < prev | next > new | recent | 2026-06 Change to browse by: cs References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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