Finding Maximal Pairs with Bounded Gap

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


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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ISSN: 0909-0878 

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