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In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete (Diagonalization complete) and H-complete (Hypercomputation complete) classes. In the paper, in the spirit of Cook/Levin/Karp, we started the population process of these new classes assigning several undecidable problems to them. We justify that some super-Turing models of computation, i.e., models going beyond Turing machines, are tremendously expressive and they allow to accept arbitrary languages over a given alphabet including those undecidable ones. We prove also that one of such super-Turing models of computation - the $-Calculus, designed as a tool for automatic problem solving and automatic programming, has also such tremendous expressiveness. We investigate also completeness of cost metrics and meta-search algorithms in $-calculus. [ABSTRACT FROM AUTHOR]

This paper is devoted to the problem of class imbalance in machine learning, focusing on the intrusion detection of rare classes in computer networks. The problem of class imbalance occurs when one class heavily outnumbers examples from the other classes. In this paper, we are particularly interested in classifiers, as pattern recognition and anomaly detection could be solved as a classification problem. As still a major part of data network traffic of any organization network is benign, and malignant traffic is rare, researchers therefore have to deal with a class imbalance problem. Substantial research has been undertaken in order to identify these methods or data features that allow to accurately identify these attacks. But the usual tactic to deal with the imbalance class problem is to label all malignant traffic as one class and then solve the binary classification problem. In this paper, however, we choose not to group or to drop rare classes but instead investigate what could be done in order to achieve good multi-class classification efficiency. Rare class records were up-sampled using SMOTE method (Chawla et al., 2002) to a preset ratio targets. Experiments with the 3 network traffic datasets, namely CIC-IDS2017, CSE-CIC-IDS2018 (Sharafaldin et al., 2018) and LITNET-2020 (Damasevicius et al., 2020) were performed aiming to achieve reliable recognition of rare malignant classes available in these datasets. Popular machine learning algorithms were chosen for comparison of their readiness to support rare class detection. Related algorithm hyper parameters were tuned within a wide range of values, different data feature selection methods were used and tests were executed with and without over-sampling to test the multiple class problem classification performance of rare classes. Machine learning algorithms ranking based on Precision, Balanced Accuracy Score, G ¯ , and prediction error Bias and Variance decomposition, show that decision tree ensembles (Adaboost, Random Forest Trees and Gradient Boosting Classifier) performed best on the network intrusion datasets used in this research. [ABSTRACT FROM AUTHOR]

In some cases of using multi-criteria decision making methods for solving real-world problems ratings of alternatives cannot be determined precisely, and that is why they are expressed in the form of intervals. Therefore, the aim of this paper is to extend the MOORA method for solving decision making problems with interval data. By extending the ratio system part of MOORA method, an algorithm to determine the most preferable alternative among all possible alternatives, when performance ratings are given as intervals, is presented. Finally, an example is shown to highlight the proposed procedure, at the end of this paper. [ABSTRACT FROM AUTHOR]

We study the query version of constrained minimum link paths between two points inside a simple polygon P with n vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning P into a number of faces of equal link distance from a point, called a link-based shortest path map (SPM). Initially, we solve this problem for two given points s, t and a query point q. Then, the proposed solution is extended to a general case for three arbitrary query points s, t and q. In the former, we propose an algorithm with O(n) preprocessing time. Extending this approach for the latter case, we develop an algorithm with O(n3) preprocessing time. The link distance of a q-visible path between s, t as well as the path are provided in time O(log n) and O(m + log n), respectively, for the above two cases, where m is the number of links. [ABSTRACT FROM AUTHOR]

We first design an (n2) solution for finding a maximum induced matching in permutation graphs given their permutation models, based on a dynamic programming algorithm with the aid of the sweep line technique. With the support of the disjoint-set data structure, we improve the complexity to (m+n). Consequently, we extend this result to give an (m+n) algorithm for the same problem in trapezoid graphs. By combining our algorithms with the current best graph identification algorithms, we can solve the MIM problem in permutation and trapezoid graphs in linear and (n2) time, respectively. Our results are far better than the best known (mn) algorithm for the maximum induced matching problem in both graph classes, which was proposed by Habib et al. [ABSTRACT FROM AUTHOR]