Optimally Computing Compressed Indexing Arrays Based on the Compact Directed Acyclic Word Graph

Hiroki Arimura, Shunsuke Inenaga, Yasuaki Kobayashi, Yuto Nakashima, Mizuki Sue

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.