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| Title | Incongruity-Sensitive Access to Highly Compressed Strings |
| Authors | Fernando Cicalese, Travis Gagie, Zsuzsanna Lipták, Gonzalo Navarro, Nicola Prezza, Cristian Urbina |
| Publication date | 2026 |
| Abstract | Random access to highly compressed strings---represented by straight-line programs or Lempel-Ziv parses, for example---is a well-studied topic. Random access to such strings in strongly sublogarithmic time is impossible in the worst case, but previous authors have shown how to support faster access to specific characters and their neighbourhoods. In this paper we explore whether, since better compression can impede access, we can support faster access to \textcolor{black}{less compressible} substrings of highly compressed strings. We first show how, given a run-length compressed straight-line program (RLSLP) of size $g_{rl}$ or a block tree of size $L$, we can build an $O (g_{rl})$-space or an $O (L)$-space data structure, respectively, that supports access to any character in time logarithmic in the length of the longest repeated substring containing that character. That is, the more ``incongruous'' a character is with respect to the characters around, the faster we can support access to it. We then prove a similar but more powerful and sophisticated result for parsings in which phrases' sources do not overlap much larger phrases, with the query time depending also on the number of phrases we must copy from their sources to obtain the queried character. |
| Pages | article 123 (track A) |
| Conference name | Annual European Symposium on Algorithms |
| Publisher | Springer-Verlag (Berlin/Heidelberg, Germany) |