International Conference Papers

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    Smaller Fully-Functional Bidirectional BWT Indexes
    (Springer Nature, 2020-09-17) Belazzougui,, Djamal; Cunial, Fabio
    Burrows-Wheeler indexes that support both extending and contracting any substring of the text $T$ of length $n$ on which they are built, in any direction, provide substantial flexibility in traversing the text and can be used to implement several algorithms. The practical appeal of such indexes is contingent on them being compact, and current designs that are sensitive to the compressibility of the input take either $O(e+\REV{e})$ words of space, where $e$ and $\REV{e}$ are the number of right and left extensions of the maximal repeats of $T$, or $O(r\log(n/r)+\REV{r}\log(n/\REV{r}))$ words, where $r$ and $\REV{r}$ are the number of runs in the Burrows-Wheeler transform of $T$ and of its reverse. In this paper we describe a fully-functional bidirectional index that takes $O(m+r+\REV{r})$ words, where $m$ is the number of maximal repeats of $T$, as well as a variant that takes $O(r+\REV{r})$ words.
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    Fully-Functional Bidirectional Burrows-Wheeler Indexes and Infinite-Order De Bruijn Graphs
    (Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2019-06-18) Belazzougui, Djamal; Cunial, Fabio
    Given a string T on an alphabet of size σ, we describe a bidirectional Burrows-Wheeler index that takes O(|T| log σ) bits of space, and that supports the addition and removal of one character, on the left or right side of any substring of T, in constant time. Previously known data structures that used the same space allowed constant-time addition to any substring of T, but they could support removal only from specific substrings of T. We also describe an index that supports bidirectional addition and removal in O(log log |T|) time, and that takes a number of words proportional to the number of left and right extensions of the maximal repeats of T. We use such fully-functional indexes to implement bidirectional, frequency-aware, variable-order de Bruijn graphs with no upper bound on their order, and supporting natural criteria for increasing and decreasing the order during traversal.