Finding Maximal Pairs with Bounded Gap

Gerth Stølting Brodal
Rune B. Lyngsø
Christian N. S. Pedersen
Jens Stoye

April 1999


A pair in a string is the occurrence of the same substring twice. A pair is maximal if the two occurrences of the substring cannot be extended to the left and right without making them different. The gap of a pair is the number of characters between the two occurrences of the substring. In this paper we present methods for finding all maximal pairs under various constraints on the gap. In a string of length $n$ we can find all maximal pairs with gap in an upper and lower bounded interval in time $O(n \log n + z)$ where $z$ is the number of reported pairs. If the upper bound is removed the time reduces to $O(n + z)$. Since a tandem repeat is a pair where the gap is zero, our methods can be seen as a generalization of finding tandem repeats. The running time of our methods equals the running time of well known methods for finding tandem repeats

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