Lcp-values, lcp-intervals, and maximal repeatsare powerful tools in various string processing tasks and have a wide variety of applications . Although many researchers have focused on developing enumeration algorithms for them, those algorithms are inefficient in that the space usage is proportional to the length of the input string. Recently, the run-length-encoded Burrows-Wheeler transform (RLBWT) has attracted increased attention in string processing, and various algorithms on the RLBWT have been developed. Developing enumeration algorithms for lcp-intervals, lcp-values, and maximal repeats on the RLBWT, however, remains a challenge. In this paper, we present the first such enumeration algorithms with space usage not proportional to the string length. The complexities of our enumeration algorithms are O(n \log \log (n/r)) time and  O(r ) words of working space for string length n and RLBWT size r .
Enumerating characteristic substrings (e.g., maximal repeats, minimal unique substrings, and minimal absent words) in a given string has been an important research topic because there are a wide variety of applications in various areas such as string processing and computational biology. Although several enumeration algorithms for characteristic substrings have been proposed, they are not space-efficient in that their space-usage is proportional to the length of an input string. Recently, the run-length encoded Burrows-Wheeler transform (RLBWT) has attracted increased attention in string processing, and various algorithms for the RLBWT have been developed. Developing enumeration algorithms for characteristic substrings with the RLBWT, however, remains a challenge. In this paper, we present r-enum (RLBWT-based enumeration), the first enumeration algorithm for characteristic substrings based on RLBWT. R-enum runs in O(n \log \log (n/r)) time and with O(r \log n) bits of working space for string length n and number r of runs in RLBWT, where r is expected to be significantly smaller than n for highly repetitive strings (i.e., strings with many repetitions). Experiments using a benchmark dataset of highly repetitive strings show that the results of r-enum are more space-efficient than the previous results. In addition, we demonstrate the applicability of r-enum to a huge string by performing experiments on a 300-gigabyte string of 100 human genomes .
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