A Different Proof of Crochemore-Ilie Lemma Concerning Microruns
نویسندگان
چکیده
We present a different computational proof of the estimate of the number of microruns established in a recent CrochemoreIlie paper. The original proof in Crochemore-Ilie paper relies on computational means, and thus our proof provides an independent verification of the fact. We also introduce a notion of R-cover that is essential to our approach. The hope is that a further analysis of R-covers will lead to a non-computational proof of the upper bound of the number of microruns.
منابع مشابه
Asymptotic behavior of the numbers of runs and microruns
The notion of run (also called maximal repetition) allows a compact representation of the set of all tandem periodicities, even fractional, in a string. Since the work of Kolpakov and Kucherov in [8, 9], it is known that ρ(n), the maximum number of runs in a string, is linear in the length n of the string. Lower bounds haven been provided by Franek et al. and Matsubara et al. (0.9445...) [5, 6,...
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