In this paper, we present the data structure that implements the Self-Balanced Binary Search Tree with strings as keys and quantum comparing procedure. We cannot use the standard Self-Balanced Binary Search because of an error probability for the quantum comparing procedure. We can solve the issue using the standard success probability boosting technique. The presented data structure is more effective (in terms of running time) than using boosting technique. We apply the data structure for the Most Frequently String problem. So, we obtain a quantum algorithm for the problem that is faster than the existing quantum algorithm, and the best classical algorithm in the case of a significant part of the input strings (we mean O(n)) has a length that is at least ω((log n)2). Here n means the number of strings in a collection.
In this paper, we consider the “Shortest Superstring Problem”(SSP) or the “Shortest Common Superstring Problem”(SCS). The problem is as follows. For a positive integer n, a sequence of n strings S = (s1, . . . , sn) is given. We should construct the shortest string t (we call it superstring) that contains each string from the given sequence as a substring. The problem is connected with the sequence assembly method for reconstructing a long DNA sequence from small fragments. We present a quantum algorithm with running time O∗(1.728n). Here O∗ notation does not consider polynomials of n and the length of t.
In this work, we consider the performance of using a quantum algorithm to predict the result of a binary classification problem when a machine learning model is an ensemble of any simple classifiers. This approach is faster than classical prediction and uses quantum and classical computing, but it is based on a probabilistic algorithm. Let N be the number of classifiers from an ensemble model and O(T) be the running time of prediction of one classifier. In classical case, the final result is obtained by ”averaging” outcomes of all ensemble model’s classifiers. The running time in classical case is O (N · T). We propose an algorithm that works in
O (√N · T ).
We consider online algorithms. Typically the model is investigated with respect to competitive ratio. In this paper, we explore algorithms with small memory. We investigate two-way automata as a model for online algorithms with restricted memory. We focus on quantum and classical online algorithms. We show that there are problems that can be better solved by two-way automata with quantum and classical states than classical two-way automata in the case of sublogarithmic memory (sublinear size).
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