Grammar Index by Induced Suffix Sorting

FM-Indexing Grammars Induced by Suffix Sorting for Long Patterns

“…However, this approach seems to be rather impractical, and up to now nobody has considered implementing it. Related to our work is the grammar indexes of Akagi et al [1] and Díaz-Domínguez et al [14], which are also based on the GCIS grammar, where the latter is based on results of Christiansen et al [7]. They also use similar techniques for extracting non-terminals from the pattern grammar, for which they can be sure of that these appear in the text grammar.…”

“…We call this factorization LMS factorization. By replacing each factor T x by the lexicographic rank of its respective LMS substring 1 , we obtain a string T (1) of these ranks. We recurse on T (1) until we obtain a string T (t T −1) whose rank-characters are all unique or whose LMS factorization consists of at most two factors.…”

“…By replacing each factor T x by the lexicographic rank of its respective LMS substring 1 , we obtain a string T (1) of these ranks. We recurse on T (1) until we obtain a string T (t T −1) whose rank-characters are all unique or whose LMS factorization consists of at most two factors. If we, instead of assigning ranks, assign each LMS substring a non-terminal, and recurse on a string of non-terminals, we obtain a grammar G T that is factorizing.…”

“…We obtain the grammar G T with the following rules: A → aac, B → ab, C → ac, D → b, and E → bc. The grammar has σ (1) := 5 non-terminals on height 1. By replacing the LMS substrings with the respective non-terminals, we obtain the string T (1) := DCBCAEE.…”

“…Regarding the space, the grammar captures the compressibility far better than the run-length compression of the BWT built on the plain text. Here, we leverage certain properties of the GCIS (grammar compression by induced suffix sorting) grammar [36], which have been discovered by Akagi et al [1] and Díaz-Domínguez et al [14] for determining non-terminals of the text matching portions of the pattern.…”