Large-scale detection of repetitions

Combinatorics on words began more than a century ago with a demonstration that an infinitely long string with no repetitions could be constructed on an alphabet of only three letters. Computing all the repetitions (such as ⋯ TTT ⋯ or ⋯ CGACGA ⋯ ) in a given string x of length n is one of the oldest and most important problems of computational stringology, requiring time in the worst case. About a dozen years ago, it was discovered that repetitions can be computed as a by-product of the Θ ( n )-time computation of all the maximal periodicities or runs in x . However, even though the computation is linear, it is also brute force: global data structures, such as the suffix array , the longest common prefix array and the Lempel–Ziv factorization , need to be computed in a preprocessing phase. Furthermore, all of this effort is required despite the fact that the expected number of runs in a string is generally a small fraction of the string length. In this paper, I explore the possibility that repetitions (perhaps also other regularities in strings) can be computed in a manner commensurate with the size of the output.

Large-scale detection of repetitions Journal Articles