Abstract
A Straight-Line Program (SLP) \(\mathcal {G}\) for a string \(\mathcal {T}\) is a context-free grammar (CFG) that derives \(\mathcal {T}\) only, which can be considered as a compressed representation of \(\mathcal {T}\).In this paper, we show how to encode \(\mathcal {G}\) in \(n \lceil \lg N \rceil + (n + n') \lceil \lg (n+\sigma ) \rceil + 4n - 2n' + o(n)\) bits to support random access queries of extracting \(\mathcal {T}[p..q]\) in worst-case \(O(\log N + q - p)\) time, where N is the length of \(\mathcal {T}\), \(\sigma \) is the alphabet size, n is the number of variables in \(\mathcal {G}\) and \(n' \le n\) is the number of symmetric centroid paths in the DAG representation for \(\mathcal {G}\).
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Notes
- 1.
Note that \( in\_rank \) queries in [11] work only for the nodes that have at least two children.
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Acknowledgements
This work was supported by JSPS KAKENHI (Grant Numbers 22K11907 and 24K02899) and JST AIP Acceleration Research JPMJCR24U4, Japan.
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Takasaka, A., I, T. (2025). Space-Efficient SLP Encoding for O(log N)-Time Random Access. 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_25
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