Compressed Dictionary Matching on Run-Length Encoded Strings
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909768807874560 |
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| author | Bille, Philip Gørtz, Inge Li Puglisi, Simon J. Tarnow, Simon R. |
| author_facet | Bille, Philip Gørtz, Inge Li Puglisi, Simon J. Tarnow, Simon R. |
| contents | Given a set of pattern strings $\mathcal{P}=\{P_1, P_2,\ldots P_k\}$ and a text string $S$, the classic dictionary matching problem is to report all occurrences of each pattern in $S$. We study the dictionary problem in the compressed setting, where the pattern strings and the text string are compressed using run-length encoding, and the goal is to solve the problem without decompression and achieve efficient time and space in the size of the compressed strings. Let $m$ and $n$ be the total length of the patterns $\mathcal{P}$ and the length of the text string $S$, respectively, and let $\overline{m}$ and $\overline{n}$ be the total number of runs in the run-length encoding of the patterns in $\mathcal{P}$ and $S$, respectively. Our main result is an algorithm that achieves $O( (\overline{m} + \overline{n})\log \log m + \mathrm{occ})$ expected time, and $O(\overline{m})$ space, where $\mathrm{occ}$ is the total number of occurrences of patterns in $S$. This is the first non-trivial solution to the problem. Since any solution must read the input, our time bound is optimal within an $\log \log m$ factor. We introduce several new techniques to achieve our bounds, including a new compressed representation of the classic Aho-Corasick automaton and a new efficient string index that supports fast queries in run-length encoded strings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compressed Dictionary Matching on Run-Length Encoded Strings Bille, Philip Gørtz, Inge Li Puglisi, Simon J. Tarnow, Simon R. Data Structures and Algorithms Given a set of pattern strings $\mathcal{P}=\{P_1, P_2,\ldots P_k\}$ and a text string $S$, the classic dictionary matching problem is to report all occurrences of each pattern in $S$. We study the dictionary problem in the compressed setting, where the pattern strings and the text string are compressed using run-length encoding, and the goal is to solve the problem without decompression and achieve efficient time and space in the size of the compressed strings. Let $m$ and $n$ be the total length of the patterns $\mathcal{P}$ and the length of the text string $S$, respectively, and let $\overline{m}$ and $\overline{n}$ be the total number of runs in the run-length encoding of the patterns in $\mathcal{P}$ and $S$, respectively. Our main result is an algorithm that achieves $O( (\overline{m} + \overline{n})\log \log m + \mathrm{occ})$ expected time, and $O(\overline{m})$ space, where $\mathrm{occ}$ is the total number of occurrences of patterns in $S$. This is the first non-trivial solution to the problem. Since any solution must read the input, our time bound is optimal within an $\log \log m$ factor. We introduce several new techniques to achieve our bounds, including a new compressed representation of the classic Aho-Corasick automaton and a new efficient string index that supports fast queries in run-length encoded strings. |
| title | Compressed Dictionary Matching on Run-Length Encoded Strings |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2509.03265 |