Improved Upper Bounds on all Maximal $\alpha$-gapped Repeats and Palindromes
نویسندگان
چکیده
We show that the number of all maximal α-gapped repeats and palindromes of a word of length n is at most 3(π/6 + 5/2)αn and 7(π/6 + 1/2)αn − 5n− 1, respectively.
منابع مشابه
Efficiently Finding All Maximal alpha-gapped Repeats
For α ≥ 1, an α-gapped repeat in a word w is a factor uvu of w such that |uv| ≤ α|u|; the two factors u in such a repeat are called arms, while the factor v is called gap. Such a repeat is called maximal if its arms cannot be extended simultaneously with the same symbol to the right or, respectively, to the left. In this paper we show that the number of maximal α-gapped repeats that may occur i...
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Following (Kolpakov et al., 2013; Gawrychowski and Manea, 2015), we continue the study of α-gapped repeats in strings, defined as factors uvu with |uv| ≤ α|u|. Our main result is the O(αn) bound on the number of maximal α-gapped repeats in a string of length n, previously proved to be O(αn) in (Kolpakov et al., 2013). For a closely related notion of maximal δ-subrepetition (maximal factors of e...
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