Download e-book for kindle: Algorithms on Strings, Trees and Sequences: Computer Science by Dan Gusfield

By Dan Gusfield

ISBN-10: 0521585198

ISBN-13: 9780521585194

Typically a space of analysis in computing device technological know-how, string algorithms have, lately, turn into an more and more very important a part of biology, quite genetics. This quantity is a entire examine desktop algorithms for string processing. as well as natural computing device technological know-how, Gusfield provides wide discussions on organic difficulties which are solid as string difficulties and on equipment built to unravel them. this article emphasizes the basic rules and strategies important to today's functions. New methods to this complicated fabric simplify tools that in past times were for the expert on my own. With over four hundred routines to augment the fabric and advance extra issues, the publication is appropriate as a textual content for graduate or complex undergraduate scholars in machine technological know-how, computational biology, or bio-informatics.

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Additional resources for Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology

Example text

Given the answer to the previous exercise, it is natural to conjecture that Zk always equals spi, where / is the largest position such that sp, maps to k. Show that this is not true. Given an example using at least three distinct characters. Stated another way, give an example to show that Zk can be greater than zero even when there is no position ;' such that sp; maps to k. 18. Recall that rk^ is known at the start of iteration k of the Z algorithm (when Zk is computed), but rk is known only at the end of iteration k.

A better compromise, below, is possible. During preprocessing, scan P from right to left collecting, for each character x in the alphabet, a list of the positions where x occurs in P. Since the scan is right to left, each list will be in decreasing order. For example, if P = abacbabc then the list for character a is 6, 3, 1. These lists are accumulated in O(n) time and of course take only O(n) space. During the search stage of the Boyer-Moore algorithm if there is a mismatch at position / of P and the mismatching character in T is x, scan x's list from the top until we reach the first number less than i or discover there is none.

Further, if x never occurs in P, then we can shift P completely past the point of mismatch in T. In these cases, some characters of T will never be examined and the method will actually run in "sublinear" time. This observation is formalized below. Definition For each character x in the alphabet, let R(x) be the position of right-most occurrence of character x in P. R(x) is defined to be zero if x does not occur in P. It is easy to preprocess P in 0{ri) time to collect the R{x) values, and we leave that as an exercise.

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Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology by Dan Gusfield

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