Efficient Parallel Algorithms for String Comparison

Abstract: The aim of the work is to analyze changes during the evolution of those pre-microRNAs that are associated with long-term memory and learning in mammals. Large changes are observed in the pre-microRNAs mir-195 and mir-206 in mouse-like rodents (superfamily Muroidea) and in opossum. But the changes are small in all primates. Moreover, for mir-206, changes were shown to be related to the logarithm of maximum life span. We suggest a significant weakening of the effect of stabilizing selection on mir-206 in species with small maximum life span. In contrast, both mir-134 and mir-182 are more conservative. Their small changes are not related to maximum life span. Changes in the secondary structure of pre-microRNA are also considered. For this study, the authors developed an algorithm to truncate the input sequence to imperfect palindrome that is close to a perfect palindrome and is obtained by removing a prefix or suffix when possible. Such an imperfect palindrome roughly corresponds to an RNA hairpin. It is important that the palindrome is delimited during the optimization. Software implementation of the considered algorithm is created in Python. The programs are available at lab6.iitp.ru/-/pali and lab6.iitp.ru/-/trimmers. Searching for a perfect palindrome, close in the Levenshtein metric to the original sequence, often yields several optimal palindromes. In this way, for mir-195, a relationship was shown between the number of optimal palindromes and the logarithm of maximum life span. There was no such relationship for the mir-134, mir-182, and mir-206. Note that mir-195 and mir-206 differ from each other in the type of changes.

TL;DR: An algorithm is presented which solves the string-to-string correction problem in time proportional to the product of the lengths of the two strings.

TL;DR: The problem of finding a longest common subsequence of two strings has been solved in quadratic time and space and an algorithm is presented which will solve this problem in QuadraticTime and in linear space.

TL;DR: An algorithm is described for computing the edit distance between two strings of length n and m, n ⪖ m, which requires O(n · max(1, mlog n) steps whenever the costs of edit operations are integral multiples of a single positive real number and the alphabet for the strings is finite.

TL;DR: Multidimensional divide-and-conquer is discussed, an algorithmic paradigm that can be instantiated in many different ways to yield a number of algorithms and data structures for multidimensional problems.