R. Kolpakov and G. Kucherov. On maximal repetitions in words. J of Discrete Algorithms, 1(1):159--186, 2000. Home/Search Document Details and Download
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Finding approximate repetitions under Hamming distance - Kolpakov, Kucherov (2001) (2 citations) Self-citation (Kolpakov Kucherov) (Correct)
....squares (i.e. subwords uu where u is not itself a repetition v k for k 2) then a word may contain O(n log n) of them and this bound is tight. All primitive squares can be found in time O(n S) where S is their number [Kos94, SG98, KK99a] hence in the worst case time O(n log n) In [KK99b, KK99a] we studied maximal repetitions (see also [ML84, Mai89] Those can be viewed as maximal runs of squares [IMS97, SG98] i.e. series of squares of equal length shifted by one letter one with respect to another. For example, bcbacacacaab contains a maximal repetition acacaca which is a ....
....shifted by one letter one with respect to another. For example, bcbacacacaab contains a maximal repetition acacaca which is a succession of four squares : acac, caca, acac, caca. Thus, the set of maximal repetitions can be regarded as an encoding of all tandem repeats in the string. We showed [KK99b] that this encoding is more compact in the worst case, as there are only O(n) maximal repetitions in words of length n. Moreover, all of them can be found in time O(n) KK99a] More recently, searching for repetitions in a string received a new motivation, due to the biosequence analysis ....
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R. Kolpakov and G. Kucherov. On maximal repetitions in words. In Proceedings of the 12-th International Symposium on Fundamentals of Computation Theory,
Maximal repetitions and Application to DNA sequences - Giraud, Kucherov (2000) Self-citation (Kucherov) (Correct)
....with i = 2: Compute l = u(i) 2 u(i 1) Let t be the suffix of u(1) u(i 1) of length l, Search, using Main and Lorentz s extension functions, the repetitions starting in t and ending in u(i) 1. 4 Number of repetitions Kolpakov and Kucherov recently proved the following theorem [10] : Theorem 3 (Kolpakov and Kucherov) The number of maximal repetitions in a word is linear in the word length. The proof [10] is quite technical. In fact, the exponent sum of such repetitions is also linear, as showed in [9] 1.5 Putting all together : the Main Kolpakov Kucherov (MKK) ....
....Lorentz s extension functions, the repetitions starting in t and ending in u(i) 1.4 Number of repetitions Kolpakov and Kucherov recently proved the following theorem [10] Theorem 3 (Kolpakov and Kucherov) The number of maximal repetitions in a word is linear in the word length. The proof [10] is quite technical. In fact, the exponent sum of such repetitions is also linear, as showed in [9] 1.5 Putting all together : the Main Kolpakov Kucherov (MKK) algorithm In [9] Kolpakov and Kucherov proposed an extension of Main s algorithm to find all maximal repetitions. Algorithm 2 (MKK ....
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KOLPAKOV, R., AND KUCHEROV, G. On maximal repetitions in words. In Proceedings of the 12th International Symposium on Fundamentals of Computation Theory, 1999, Iasi (Romania) (1999), vol. 1684 of LNCS, pp. 374--385.
Finding Repeats With Fixed Gap - Kolpakov, Kucherov Self-citation (Kolpakov Kucherov) (Correct)
.... compression [Sto88] or biological sequence analysis [Gus97] A great deal of work, in word combinatorics and string matching, has been devoted to contiguous repetitions, when a fragment is repeated contiguously two or more times [Cro81, Sli83, Cro83, AP83, ML84, ML85, Mai89, Kos94, IMS97, SG98a, KK99b, SG98b, KK99a] A simplest form of contiguous repetition is a square (tandem repeat) which is a subword of the form uu. On the other hand, some applications bring up the problem of nding subwords repeated in a word in a possibly non contiguous way. As an example, it is well known that the sux ....
....0 ; w 00 ) with period p i LPR(p) LSF (p) p. When this inequality holds, there is a family of quasi squares with period p from QS l m (w 0 ; w 00 ) with the left roots starting at positions [m LSF (p) m minfLPR(p) pg p] 1 Formal de nitions of these notions can be found in [KK99b] 2 This families are analogous to runs of squares in [IMS97, SG98a] 3 To use Lemma 1 as an algorithm for computing QS l m (w 0 ; w 00 ) we have to compute values LPR(p) LSF (p) for p = 1; m. All these values can be computed eciently in time O(m) using a variation of the ....
R. Kolpakov and G. Kucherov. On maximal repetitions in words. In Proceedings of the 12-th International Symposium on Fundamentals of Computation Theory, 1999, Iasi (Romania), Lecture Notes in Computer Science, August 30 - September 3 1999.
International Journal of Foundations of Computer Science - Vol No World (Correct)
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R. Kolpakov and G. Kucherov. On maximal repetitions in words. J of Discrete Algorithms, 1(1):159--186, 2000.
Two-Pattern Strings - Franek, Jiang, Lu, Smyth (2002) (Correct)
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Roman Kolpakov & Gregory Kucherov, On maximal repetitions in words, J. Discrete Algorithms 1 (2000) 159-186.
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