Wheeler maps

Motivated by challenges in pangenomic read alignment, we propose a generalization of Wheeler graphs that we call Wheeler maps. A Wheeler map stores a text \(T[1..n]\) and an assignment of tags to the characters of \(T\) such that we can preprocess a pattern \(P[1..m]\) and then, given \(i\) and \(j\), quickly return all the distinct tags labeling the first characters of the occurrences of \(P[i..j]\) in \(T\). For the applications that most interest us, characters with long common contexts are likely to have the same tag, so we consider the number \(t\) of runs in the list of tags sorted by their characters' positions in the Burrows-Wheeler Transform (BWT) of \(T\). We show how, given a straight-line program with \(g\) rules for \(T\), we can build an \(O(g + r + t)\)-space Wheeler map, where \(r\) is the number of runs in the BWT of \(T\), with which we can preprocess a pattern \(P[1..m]\) in \(O(m \log n)\) time and then return the \(k\) distinct tags for \(P[i..j]\) in optimal \(O(k)\) time for any given \(i\) and \(j\). We show various further results related to prioritizing the most frequent tags.