k-Abelian Pattern Matching

Two words are called \(k\)-abelian equivalent, if they share the same multiplicities for all factors of length at most \(k\). We present an optimal linear time algorithm for identifying all occurrences of factors in a text that are \(k\)-abelian equivalent to some pattern. Moreover, an optimal algorithm for finding the largest \(k\) for which two words are \(k\)-abelian equivalent is given. Solutions for various online versions of the \(k\)-abelian pattern matching problem are also proposed.

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