An O(n log n) algorithm for finding dissimilar strings

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Abstract

Let Σ be a finite alphabet and x ϵn. A string y ϵm is said to be k-dissimilar to x, if no k length substring of x is equal to any k length substring of y. We present an O(n log n) algorithm which on input x ϵn and an integer mn outputs an integer k and y ϵm such that:

  • 1.

    (1) y is k-dissimilar to x.

  • 2.

    (2) There does not exist a string z of length m which is k − 1 dissimilar to x.

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