Abstract
In this paper, we present the first study of the computational complexity of converting an automata-based text index structure, called the Compact Directed Acyclic Word Graph (CDAWG), of size e for a text T of length n into other text indexing structures for the same text, suitable for highly repetitive texts: the run-length BWT of size r, the irreducible PLCP array of size r, and the quasi-irreducible LPF array of size e, as well as the lex-parse of size O(r) and the LZ77-parse of size z, where \(r, z \leqslant e\). As main results, we showed that the above structures can be optimally computed from either the CDAWG for T stored in read-only memory or its self-index version of size e without a text in O(e) worst-case time and words of working space. To obtain the above results, we devised techniques for enumerating a particular subset of suffixes in the lexicographic and text orders using the forward and backward search on the CDAWG by extending the result by Belazzougui et al. in 2015.
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Notes
- 1.
The n-th Thue-Morse word is \(\tau _n = \varphi ^n(0)\) for the morphism \(\varphi (0) = 01\) and \(\varphi (1) = 10\).
References
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Acknowledgments
The authors thank the anonymous reviewers for their comments which greatly improved this paper. The first author is also grateful to Hideo Bannai for information on conversion between text indexes, and to Mitsuru Funakoshi for discussion on the sensitivity of text indexes.
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Arimura, H., Inenaga, S., Kobayashi, Y., Nakashima, Y., Sue, M. (2023). Optimally Computing Compressed Indexing Arrays Based on the Compact Directed Acyclic Word Graph. In: Nardini, F.M., Pisanti, N., Venturini, R. (eds) String Processing and Information Retrieval. SPIRE 2023. Lecture Notes in Computer Science, vol 14240. Springer, Cham. https://doi.org/10.1007/978-3-031-43980-3_3
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