Maximal pair

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In computer science, a maximal pair is a tuple (p_1, p_2, l), such that, given a string S of length n, S[p_1..p_1+l-1]=S[p_2..p_2+l-1], but S[p_1-1] \neq S[p_2-1] and S[p_1+l] \neq S[p_2+l]. A maximal repeat is a string represented by such tuple. A supermaximal repeat is a maximal repeat never occurring as a proper substring of another maximal repeat. Both maximal pairs, maximal repeats and supermaximal repeats can be found in \Theta(n+z) time using a suffix tree,[1] if there are z such structures.



(2,6,3) and (6,10,3) are maximal pairs, but (2,10,3) is not, as y follows both substrings. abc and abcy are maximal repeats, but only abcy is a supermaximal repeat.


  1. ^ Gusfield, Dan (1999) [1997]. Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology. USA: Cambridge University Press. p. 143. ISBN 0-521-58519-8. 

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