By Alexander S. Kulikov, Sergei O. Kuznetsov, Pavel Pevzner

This booklet constitutes the refereed complaints of the twenty fifth Annual Symposium on Combinatorial trend Matching, CPM 2014, held in Moscow, Russia, in June 2014. The 28 revised complete papers offered including five invited talks have been rigorously reviewed and chosen from fifty four submissions. The papers tackle problems with looking and matching strings and extra complex styles reminiscent of bushes; commonplace expressions; graphs; element units; and arrays. The objective is to derive combinatorial houses of such constructions and to take advantage of those houses that allows you to in achieving greater functionality for the corresponding computational difficulties. The assembly additionally bargains with difficulties in computational biology; information compression and information mining; coding; details retrieval; traditional language processing; and development recognition.

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Extra resources for Combinatorial Pattern Matching: 25th Annual Symposium, CPM 2014, Moscow, Russia, June 16-18, 2014. Proceedings

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For = 1 the statement holds trivially. Consider ≥ 2. Let m, as before, denote /2 − 1. If is even, then + 1 is odd and we have Sj +1 = 3 · 2m + (j mod 2m ) < 4 · 2m ≤ 2 · (2 · 2m + (j mod 2m )) = 2 Sj while for odd Sj +1 = 2·2m+1 +(j mod 2m+1 ) < 3·2m+1 ≤ 2·(3 · 2m + (j mod 2m )) = 2 Sj . 34 M. Babenko et al. Fact 4. For 1 ≤ i < j ≤ n, the value α(i, j) can be computed in constant time. Proof. j]| . j]|. Thus α(i, j) ∈ {2m − 1, 2m, 2m + 1}, and we can verify in constant time which of these values is the correct one.

We say that a prefix of the string is a palindrome with k mismatches if changing k locations in the prefix will make it a palindrome. Partly supported by NSF grant CCR-09-04581, ISF grant 347/09, and BSF grant 2008217. Partly supported by a Bar Ilan University President Fellowship. D. thesis. S. O. Kuznetsov, and P. ): CPM 2014, LNCS 8486, pp. 21–29, 2014. c Springer International Publishing Switzerland 2014 22 A. Amir and B. Porat The Contributions of this Paper: 1. We define a fingerprint that recognizes a palindrome with high probability.

In particular for a pair of substrings x, y of T we can compute their longest common suffix lcs(x, y) and the largest integer α such that xα is a suffix of y. 3 Minimal Suffix Consider a string T of length n. j], which we call canonical. By Sj we denote the -th shortest canonical 32 M. Babenko et al. substring ending at the position j. j]. j], (b) Sj +1 ≤ 2 Sj for any , (c) α(i, j) and |Sj | are computable in O(1) time given i, j and , j respectively. Our data structure works for any choice of canonical substrings satisfying these properties, including the simplest one with |Sj | = min(2 −1 , j).

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