Finding Repeats With Fixed Gap

Roman Kolpakov (1) , Gregory Kucherov (1)

1 POLKA - Polynomials, Combinatorics, Arithmetic

We propose an algorithm for finding in a word all pairs of occurrences of the same subword within a given distance $r$. The obtained complexity is $O(n\log r +S)$, where $S$ is the size of the output. We also show how the algorithm can be modified in order to find all such pairs of occurrences separated by a given word. The solution uses an algorithm for finding all {\em quasi-squares} in two strings, a problem that generalizes the well-known problem of searching for squares.

Mots clés: algorithm; complexity; word; square; complexité; séquence; mot; carré; répétition à espace fixe; repeat with fixed gap; algorithme

Domaines: Autre [cs.OH]

Roman Kolpakov, Gregory Kucherov. Finding Repeats With Fixed Gap. 7th International Symposium on String Processing & Information Retrieval - SPIRE 2000, 2000, Coruna, Spain, pp.162--168. ⟨inria-00107855⟩