By Ron Shamir (auth.), Juha Kärkkäinen, Jens Stoye (eds.)
This publication constitutes the refereed complaints of the twenty third Annual Symposium on Combinatorial trend Matching, CPM 2012, held in Helsinki, Finland, in July 2012.
The 33 revised complete papers awarded including 2 invited talks have been rigorously reviewed and chosen from 60 submissions. The papers deal with problems with looking and matching strings and extra advanced styles akin to bushes, typical expressions, graphs, element units, and arrays. The objective is to derive non-trivial combinatorial homes of such buildings and to use those homes so as to both in achieving enhanced functionality for the corresponding computational difficulties or pinpoint stipulations less than which searches can't be played successfully. The assembly additionally offers with difficulties in computational biology, info compression and knowledge mining, coding, details retrieval, ordinary language processing, and trend recognition.
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Additional resources for Combinatorial Pattern Matching: 23rd Annual Symposium, CPM 2012, Helsinki, Finland, July 3-5, 2012. Proceedings
Example text
Illustration of Observation 1 b a a a b a a a a 32 M. Crochemore et al. Observation 1. Assume we have a D-tree labelled with letters a, b. Let us take only paths from a vertex in T1 to R or from R to a vertex in T2 which contain at most one b, with other edges labelled with a. Then the resulting labelled tree is a standard comb (with at most one additional branch attached to R). Corollary 1. Assume binary alphabet {a, b}. The maximum number of special squares in any tree is O(n4/3 ). Proof. By Lemma 4, it suffices to consider a D-tree D = (T1 , T2 , R) and only special D-squares in D.
A) A matrix not satisfying the C1P and such that the number of MCS is exponential in the number of rows. (b) A row intersection graph of the matrix whose vertices correspond to the rows of the matrix, and such that there exists an edge between two rows ri and rj if ri ∩ rj = ∅. From a computational point of view, the first question that arises is the following: is a given row r ∈ R included in at least one MCS ? This question has been raised in [1], recalled in [4,5] and recently solved in polynomial time O(m6 n5 (m + n)2 log(m + n)) in [3].
Similarly (pq)r+2 p is not a suffix of w. Thus u = (pq)min( ,r)+1 . In particular , r ≥ 1. Clearly (pq)k p for 2 ≤ k ≤ min( , r) + 1 are the only periodic borders of w of the type (p, q). Now it remains to show the uniqueness of the representation. Assume there was another representation w = p(qp) y (pq)r p. Since y has a prefix qp but not (qp)2 , + 1 is the largest m such that p(qp)m is a prefix of m, that is = . Similarly r = r and finally y = y. A periodic border is called maximal if it is the longest border of its periodic type.