By Alberto Apostolico, Maxime Crochemore (auth.), Johannes Fischer, Peter Sanders (eds.)
This publication constitutes the refereed court cases of the twenty fourth Annual Symposium on Combinatorial trend Matching, CPM 2013, held in undesirable Herrenalb (near Karlsruhe), Germany, in June 2013. The 21 revised complete papers provided including 2 invited talks have been rigorously reviewed and chosen from fifty one submissions. The papers deal with problems with looking out and matching strings and extra complex styles resembling bushes, general expressions, graphs, aspect units, and arrays. The aim is to derive non-trivial combinatorial houses of such constructions and to use those homes which will both in achieving more desirable functionality for the corresponding computational challenge or pinpoint stipulations below which searches can't be played successfully. The assembly additionally offers with difficulties in computational biology, info compression and knowledge mining, coding, info retrieval, usual language processing, and development recognition.
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Extra resources for Combinatorial Pattern Matching: 24th Annual Symposium, CPM 2013, Bad Herrenalb, Germany, June 17-19, 2013. Proceedings
J] eﬃciently. First, build the suﬃx array SA of T . As indicated in Section 2, SA occupies O(n) memory and can be built in O(n) time. Then compute ISA array by inverting SA. We preprocess ISA so as to answer range minimum queries over it in constant time. j] is the lexicographically minimal suﬃx among suﬃxes starting between positions i through j (inclusively). g. . ], . . ]} in O(1) time. j]. Lemma 1. j]. j]. Proof. j]. j]. m + ], and T [μ + + 1] < T [m + + 1]. j] as well. Let us show that Case (2) is impossible.
The length of a string t is denoted by |t|. For a string t = xyz, x, y and z are called a preﬁx, substring, and suﬃx of t, respectively. j] for 1 ≤ i ≤ j ≤ |t|. j] = ε if j < i. Our model of computation is the word RAM: we shall assume that the word size is at least log2 |t| , and hence operations on values representing lengths and positions of string t can be manipulated in constant time. Space complexities will be determined by the number of computer words (not bits). 40 H. Bannai et al. X7 X6 X5 X4 X5 X3 X1 X3 X3 X4 X1 X2 X1 X2 X1 X1 X2 X1 X3 X4 X3 X1 X2 X1 X2 a 1 a 2 b 3 a 4 b 5 a 6 a 7 b 8 a b a a b 9 10 11 12 13 Fig.
The contribution of this paper is as follows. Given an SLP of size n that represents a string t of length N , we present an O(n + m log m) time and space algorithm for computing the LZ78 factorization of t, where m is the number of LZ78 factors. Then we improve the space complexity to linear in n + m at the cost of increasing the time complexity √ √ to O((n + m) log m). This improves on the previous √ O(n N +m log N ) time and O(n N +m) space solution . Since m = Ω( N ), the second term is asymptotically m log m = O(m log N ) and diﬀers only by a constant factor.