Non-overlapping indexing in BWT-runs bounded space

We revisit the non-overlapping indexing problem for an efficient repetition-aware solution. The problem is to index a text $T[1..n]$, such that whenever a pattern $P[1..p]$ comes as a query, we can report the largest set of non-overlapping occurrences of P in T. A previous index by Cohen and Porat [ISAAC 2009] takes linear space and optimal $O(p+\mathrm{oc}{c}_{\mathrm{no}})$ query time, where $\mathrm{oc}{c}_{\mathrm{no}}$ denotes the output size. We present an index of size $O\left(r\right)$, where r denotes the number of runs in the Burrows Wheeler Transform (BWT) of T. The parameter r is significantly smaller than n for highly repetitive texts. The query time of our index is $O(p\log {\log }_w\sigma +\mathrm{sort}(\mathrm{oc}{c}_{\mathrm{no}}\left)\right)$, where σ denotes the alphabet size, w denotes the machine word size in bits and $\mathrm{sort}\left(x\right)$ denotes the time for sorting x integers within the range $[1,n]$. We also study the counting version of this problem.