Randomized algorithms for sequence recovery by its subsequences

<p>This Graduate work is devoted to the task of sequence reconstruction via its subsequences. The task of sequence reconstruction via its subsequences is very relevant, since a large amount of information that surrounds us can be represented as sequences, while, in the meantime, at work with it some important data could be loosed. That is why the task of sequence reconstruction via its subsequences was formulated &ndash; in order to restore the lost data.</p><p>This problem has been considered by various scholars; however, there are not so many results of its solutions because of its complexity. Probabilistic algorithms were not previously applied to this problem as a method to solve it, and this is the novelty and theoretical significance of this work.</p><p>This paper presents a new algorithm, developed by the author, which reconstruct a sequence from its subsequence and also has several optional parts. The complexity of this algorithm and how quickly it effectively solves the problem are estimated.</p><p>Also author conducted a number of numerical experiments, confirming the assessment, made ​​by him, and experimentally proving the correctness, accuracy, reliability and efficiency of the algorithm. Results are successfully analyzed and conclusions about the dependence of the correctness of the algorithm, evaluated by using several criteria, on the parameters of the original data are given.</p><p>The new algorithm &ndash; the main result of this paper - shows good results in restoring the sequence via its subsequences, especially on the full set of subwords. Therefore, it can be used in a wide range of different areas, such as biology, computer science, medicine, information security, genetics, cryptography, and especially in large amounts of telecommunication systems that use the transmission of information in the digital form.</p>