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Register a new userRepresenting the suffix tree with the CDAWG
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Added by
Djamal Belazzougui
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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Given a string $T$, it is known that its suffix tree can be represented using the compact directed acyclic word graph (CDAWG) with $e_T$ arcs, taking overall $O(e_T+e_{{overline{T}}})$ words of space, where ${overline{T}}$ is the reverse of $T$, and supporting some key operations in time between $O(1)$ and $O(log{log{n}})$ in the worst case. This representation is especially appealing for highly repetitive strings, like collections of similar genomes or of version-controlled documents, in which $e_T$ grows sublinearly in the length of $T$ in practice. In this paper we augment such representation, supporting a number of additional queries in worst-case time between $O(1)$ and $O(log{n})$ in the RAM model, without increasing space complexity asymptotically. Our technique, based on a heavy path decomposition of the suffix tree, enables also a representation of the suffix array, of the inverse suffix array, and of $T$ itself, that takes $O(e_T)$ words of space, and that supports random access in $O(log{n})$ time. Furthermore, we establish a connection between the reversed CDAWG of $T$ and a context-free grammar that produces $T$ and only $T$, which might have independent interest.
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The compact directed acyclic word graph (CDAWG) of a string $T$ of length $n$ takes space proportional just to the number $e$ of right extensions of the maximal repeats of $T$, and it is thus an appealing index for highly repetitive datasets, like collections of genomes from similar species, in which $e$ grows significantly more slowly than $n$. We reduce from $O(mlog{log{n}})$ to $O(m)$ the time needed to count the number of occurrences of a pattern of length $m$, using an existing data structure that takes an amount of space proportional to the size of the CDAWG. This implies a reduction from $O(mlog{log{n}}+mathtt{occ})$ to $O(m+mathtt{occ})$ in the time needed to locate all the $mathtt{occ}$ occurrences of the pattern. We also reduce from $O(klog{log{n}})$ to $O(k)$ the time needed to read the $k$ characters of the label of an edge of the suffix tree of $T$, and we reduce from $O(mlog{log{n}})$ to $O(m)$ the time needed to compute the matching statistics between a query of length $m$ and $T$, using an existing representation of the suffix tree based on the CDAWG. All such improvements derive from extracting the label of a vertex or of an arc of the CDAWG using a straight-line program induced by the reversed CDAWG.
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