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The research is devoted to the estimation the structural complexity of programs. The algorithm of finding cyclomatic routes for program executions is described. By now, two directions of obtaining estimates for the complexity estimates in software modules have been defined: structural and statistical. Both directions connect the value of program complexity with the labor intensity related to their development. The structural complexity of program modules is determined by the number of interacting components, the number and complexity of links between them. The complexity of a program's behavior depends to a large extent on the set of routes through which it is executed. The complexity metric obtained from these positions allows us to determine estimates of the cost of designing the program as a whole, as well as to identify the modules that are likely to contain the most errors, especially the logical ones.

Abstract The water flow optimizer (WFO) is the latest swarm intelligence algorithm inspired by the shape of water flow. Its advantages of simplicity, efficiency, and robust performance have motivated us to further enhance it. In this paper, we introduce fractional-order (FO) technology with memory properties into the WFO, called fractional-order water flow optimizer (FOWFO). To verify the superior performance and practicality of FOWFO, we conducted comparisons with nine state-of-the-art algorithms on benchmark functions from the IEEE Congress on Evolutionary Computation 2017 (CEC2017) and four real-world optimization problems with large dimensions. Additionally, tuning adjustments were made for two crucial parameters within the fractional-order framework. Finally, an analysis was performed on the balance between exploration and exploitation within FOWFO and its algorithm complexity.

In a competitive environment, the ability to rapidly and successfully scale up new business models is critical. However, research shows that many new business models fail. This research looks at hybrid methods for minimizing constraints and maximizing opportunities in large data sets by examining the multivariable that arise in user behavior. E-metric data is being used as assessment material. The analytical hierarchy process (AHP) is used in the multi-criteria decision making (MCDM) approach to identify problems, compile references, evaluate alternatives, and determine the best alternative. The multi-objectives genetic algorithm (MOGA) role analyzes and predicts data. The method is being implemented to expand the information base of the strategic planning process. This research examines business sustainability along two critical dimensions. First, consider the importance of economic, environmental, and social evaluation metrics. Second, the difficulty of gathering information will be used as a predictor for making long-term business decisions. The results show that by incorporating the complexity features of input optimization, uncertainty optimization, and output value optimization, the complexity prediction model (MPK) achieves an accuracy of 89%. So that it can be used to forecast future business needs by taking into account aspects of change and adaptive behavior toward the economy, environment, and social factors. [ABSTRACT FROM AUTHOR]

The tracking of moving objects with the use of GPS/GNSS or other techniques is relied upon in numerous applications, from health monitoring and physical activity support, to social investigations to detection of fraud in transportation. While monitoring movement, a common subtask consists in determining the object's moving periods, and its immobility periods. In this paper, we isolate the mathematical problem of automatic detection of a stop of tracking objects under the stream processing regime (ideal data processing algorithm regime) in which one is allowed to use only a constant amount of memory, while the stream of GNSS positions of the tracked object increases in size. We propose an approximation scheme of the stop detection problem based on the fuzziness in the approximation of noise level related to the position reported by GNSS. We provide a solving algorithm that determines some upper bounds for the problem's complexity. We also provide an experimental illustration of the problem at hand.

The tracking of moving objects with the use of GPS/GNSS or other techniques is relied upon in numerous applications, from health monitoring and physical activity support, to social investigations to detection of fraud in transportation. While monitoring movement, a common subtask consists in determining the object's moving periods, and its immobility periods. In this paper, we isolate the mathematical problem of automatic detection of a stop of tracking objects under the stream processing regime (ideal data processing algorithm regime) in which one is allowed to use only a constant amount of memory, while the stream of GNSS positions of the tracked object increases in size. We propose an approximation scheme of the stop detection problem based on the fuzziness in the approximation of noise level related to the position reported by GNSS. We provide a solving algorithm that determines some upper bounds for the problem's complexity. We also provide an experimental illustration of the problem at hand. [ABSTRACT FROM AUTHOR]

In the academic year 2021/2022, the State Matriculation Exam (the examination taken at the end of Secondary education to qualify for entry into University) was held for the first time for the students studying the profiling subject of Informatics in the Bulgarian secondary school. The article examines the tasks from the two sessions of the exam, which are supposed test the ability of high school students to select/create algorithms. The conditions to which a task of this type must meet and to what extent the tasks of the two exam topics satisfy these conditions are examined in detail. [ABSTRACT FROM AUTHOR]

Structural methods for program testing are described, such as branch testing, program verification, symbolic testing, and generating structural tests. An algorithm for the minimum coverage of the program graph based on the packing adjacency matrix and a specific example of the minimum coverage of the program graph are given. [ABSTRACT FROM AUTHOR]

In a recent paper (Lv and Wang, Study on proportionate flowshop scheduling with due-date assignment and position-dependent weights. Optim. Lett., 2021. https://doi.org/10.1007/s11590-020-01670-4), Lv and Wang studied due date proportionate flowshop scheduling problems with position-dependent weights. For common due date and slack due date assignments, they proved that these two problems can be solved in O (n log n) time respectively, where n is the number of jobs. For slack due date assignment, there is an error. We will show the error by a counter example and explain why it is incorrect. [ABSTRACT FROM AUTHOR]

This article considers a problem of chromosomal pathologies detection. Chromosomal pathologies are dangerous and pose a great threat for family planning. To address them, the karyotyping process is conducted. Currently this process is manual or semimanual, despite high effort and error cost. So, there is a need for automation of the process. This process (and automation algorithm) can be separated into different stages with various objectives. However, the shared element among these stages is format that allows to store and manage data efficiently. The goal of this paper is to propose such format. The paper revises peculiarities of karyotyping process and briefly describes steps of the pathology detection algorithm. It also considers common formats for bioinformatics data. However, their efficiency is debatable, since data stored in these formats is redundant for the task at hand. After that, a new custom data format is proposed. This format represents main entities involved in the process of anomaly recognition. Several fragments of algorithm are considered, and their complexity is estimated combined with proposed data format. As a result, this paper proposes a new data storage format used in a chromosome abnormalities recognition algorithm, and metrics that can be used to make measurable improvement over the proposed format. [ABSTRACT FROM AUTHOR]

We give some simple description for the finitely generated structures with P-computable isomorphic presentation; i.e., presentation computable in polynomial time. The description is close to the formulation of a Remmel and Friedman theorem. We prove that each finitely generated substructure of a P-computable structure also has a P-computable presentation. The description is applied to the classes of finitely generated semigroups, groups, unital commutative rings and fields, as well as ordered unital commutative rings and fields. We prove that every finitely generated commutative ring or a field has a P-computable presentation. [ABSTRACT FROM AUTHOR]

Although algorithmic decision support is omnipresent in many managerial tasks, a lack of algorithm transparency is often stated as a barrier to successful human–machine collaboration. In this paper, we analyze the effects of algorithm transparency on the use of advice from algorithms with different degrees of complexity. We conduct a set of laboratory experiments in which participants receive identical advice from algorithms with different levels of transparency and complexity. Our results indicate that not the algorithm itself, but the individually perceived appropriateness of algorithmic complexity moderates the effects of transparency on the use of advice. We summarize this effect as a plateau curve: While perceiving an algorithm as too simple severely harms the use of its advice, the perception of an algorithm as being too complex has no significant effect. Our insights suggest that managers do not have to be concerned about revealing algorithms that are perceived to be appropriately complex or too complex to decision‐makers, even if the decision‐makers do not fully comprehend them. However, providing transparency on algorithms that are perceived to be simpler than appropriate could disappoint people's expectations and thereby reduce the use of their advice. [ABSTRACT FROM AUTHOR]

To solve the subset sum problem, a well-known nondeterministic polynomial-time complete problem that is widely used in encryption and resource scheduling, we propose a feasible quantum algorithm that utilizes fewer qubits to encode and achieves quadratic speedup. Specifically, this algorithm combines an amplitude amplification algorithm with quantum phase estimation, and requires n + t + 1 qubits and O(2(0.5+o(1))n) operations to obtain the solution, where n is the number of elements, and t is the number of qubits used to store the eigenvalues. To verify the performance of the algorithm, we simulate the algorithm with the online quantum simulator of IBM named ibmq_simulator using Qiskit and then run it on two IBM quantum computers called ibmq_santiago and ibmq_bogota. The experimental results indicate that compared with the brute force algorithm, the proposed algorithm results in quadratic acceleration for the problem of a set S with four elements and two subsets whose sum equals target w. Using the iterator twice, we obtain success probabilities of 0.940 ± 0.004, 0.751 ± 0.040, and 0.665 ± 0.060 on the simulator, ibmq_santiago, and ibmq_bogota, respectively, and the fidelity between the theoretical and experimental quantum states is calculated to be 0.944 ± 0.002, 0.753 ± 0.017, and 0.657 ± 0.028, respectively. If the error rates of the experimental quantum logic gates can be reduced, the success probabilities of the proposed algorithm on real quantum devices can be further improved. [ABSTRACT FROM AUTHOR]

The general problem of tiling finite regions of the plane with polyominoes is NP -complete, and so the associated computational geometry problem rapidly becomes intractable for large instances. Thus, the need to reduce algorithm complexity for tiling is important and continues as a fruitful area of research. Traditional approaches to tiling with polyominoes use backtracking, which is a refinement of the 'brute-force' solution procedure for exhaustively finding all solutions to a combinatorial search problem. In this work, we combine checkerboard colouring techniques with a recently introduced integer linear programming (ILP) technique for tiling with polyominoes. The colouring arguments often split large tiling problems into smaller subproblems, each represented as a separate ILP problem. Problems that are amenable to this approach are embarrassingly parallel, and our work provides proof of concept of a parallelizable algorithm. The main goal is to analyze when this approach yields a potential parallel speedup. The novel colouring technique shows excellent promise in yielding a parallel speedup for finding large tiling solutions with ILP, particularly when we seek a single (optimal) solution. We also classify the tiling problems that result from applying our colouring technique according to different criteria and compute representative examples using a combination of MATLAB and CPLEX, a commercial optimization package that can solve ILP problems. The collections of MATLAB programs PARIOMINOES (v3.0.0) and POLYOMINOES (v2.1.4) used to construct the ILP problems are freely available for download. [ABSTRACT FROM AUTHOR]

In a recent study, Sun et al. (AOR 292:113–131, 2020) studied due-window proportionate flow shop scheduling problems with position-dependent weights. For common due-window (denoted by CONW) and slack due-window (denoted by SLKW) assignment methods, they proved that these two problems can be solved in O (n 2 log n) time respectively, where n is the number of jobs. In this paper, we consider the same problems, and our contribution is that the CONW problem can be optimally solved by a lower-order algorithm, which runs in O (n log n) time, implying an improvement of a factor of n. [ABSTRACT FROM AUTHOR]

Recurrent neural networks have found their application in a wide range of tasks related to the processing of sequential data sets, because of using of an internal state, which depends on both the current input data and the state at the previous iteration. DeepMind group proposed a new approach combining the attention mechanism and external memory. It became a big step in the development of this class of networks. The architecture called the Neural Turing Machine, as well as the later improved Differential Neural Computer (DNC) model, are an alternative to the classical Turing machine, with the exception that all its operations are differential. During all the opportunities that open, researchers faced with incomplete knowledge of its fundamental capabilities. In this thesis proposed a research method based on the use of DNC to solve basic elementary algorithms and analyzing the obtained characteristics of the model in comparison with classical algorithms for a Turing machine. The results obtained in this paper provide researchers with both practical advice on the use of DNC, shows weaknesses, and open new directions for the further improvement of this neural network architecture. [ABSTRACT FROM AUTHOR]

In a recent paper, Jiang et al. (Eng Optim 52(1):37–52, 2020) considered proportionate flowshop scheduling with position-dependent weights. For common and slack due-date assignment problems, they proved that both of these two problems can be solved in O (n 2 log n) time, where n is the number of jobs. The contribution of this paper is that we show that these two problems can be optimally solved by a lower-order algorithm, i.e., in O (n log n) time. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This work analyzes the computational complexity of algorithm BEPtoPNST which transforms a building-evacuation problem (BEP) into a time-expanded, process-network synthesis (PNST) problem. The solution of the latter is achieved by resorting to the P-graph method which exploits the combinatorial nature of a BEP. Unlike other approaches, the P-graph method provides not only the optimal solution (best evacuation route as a function of egress time), but also the best n sub-optimal solutions. For the complexity analysis, a generic processor, and a Random-access machine (RAM) model were deployed as well as a mathematical model to calculate the number and cost of the operations performed. It was observed that algorithm BEPtoPNST exhibits an asymptotic complexity of order O (T/A/(/N/-k)). When solving a BEP, however, the total complexity grows exponentially with order O (T/A/(/N/-k)) + O (2h)) in the worst case; where h represents the total number of operating units specified in the corresponding PNST problem. Nevertheless, the computational complexity can be reduced significantly when the P-graph method is deployed. [ABSTRACT FROM AUTHOR]

The quadratic forms are algebraic expressions that have important role in different areas of computer science, mathematics, physics, statistics and others. We deal with quadratic forms that are widely used in the study of algebras with finite representation type, called unit forms. Especially, we study unit forms q : Z n → Z by means of their associated edge-bipartite signed (multi)graphs without loops. A big challenge in this field is to develop efficient algorithms to recognize the type of a given unit form. Actually, most algorithms can demand a long time on this task and becomes infeasible. Our aim is to present a new strategy, do the unit form recognition through sequences of mutations in the unit form related exchange matrix P. For that, we show that the positive roots of the unit form are in the c-matrix of P. We also present an algorithm to recognize the type of a given unit form, implemented using BFS (Breadth First Search) and using powerful techniques to simplify this process. [ABSTRACT FROM AUTHOR]

The general problem of tiling finite regions of the plane with polyominoes is NP-complete, and so the associated computational geometry problem rapidly becomes intractable for large instances. Thus, the need to reduce algorithm complexity for tiling is important and continues as a fruitful area of research. Traditional approaches to tiling with polyominoes use backtracking, which is a refinement of the ‘brute-force’ solution procedure for exhaustively finding all solutions to a combinatorial search problem. In this work, we combine checkerboard colouring techniques with a recently introduced integer linear programming (ILP) technique for tiling with polyominoes. The colouring arguments often split large tiling problems into smaller subproblems, each represented as a separate ILP problem. Problems that are amenable to this approach are embarrassingly parallel, and our work provides proof of concept of a parallelizable algorithm. The main goal is to analyze when this approach yields a potential parallel speedup. The novel colouring technique shows excellent promise in yielding a parallel speedup for finding large tiling solutions with ILP, particularly when we seek a single (optimal) solution. We also classify the tiling problems that result from applying our colouring technique according to different criteria and compute representative examples using a combination of MATLAB and CPLEX, a commercial optimization package that can solve ILP problems. The collections of MATLAB programs PARIOMINOES (v3.0.0) and POLYOMINOES (v2.1.4) used to construct the ILP problems are freely available for download.

When an algorithm or a program runs on a computer, it requires some resources. The complexity of an algorithm is the measure of the resources, for some input. These complexities are usually space and time. The subject of the empirical computational complexity has been studied in the research. This article introduces GuessCompx which is an R package that performs an empirical estimation on the time and memory complexities of an algorithm or a function, and provides a reliable, convenient and simple procedure for estimation process. It tests multiple increasing-sizes samples of the user's data and attempts to fit one of seven complexity functions: O(N), O(Nˆ2), O(log(N)), etc. In addition, based on the best fit procedure using leave one out-mean squared error (LOO-MSE), it predicts the full computation time and memory usage on the whole dataset. Together with this results, a plot and a significance test are returned. Complexity is assessed with regard to the user's actual dataset through its size (and no other parameter). This article provides several examples demonstrating several cases (e.g., distance function, time series and custom function) and optimal parameters tuning. [ABSTRACT FROM AUTHOR]

The degree of dispersion of a random variable can be described by the variance, which reflects the distance of the random variable from its mean. However, the time complexity of the traditional variance calculation algorithm is O(n), which results from full calculation of all samples. When the number of samples increases or on the occasion of high speed signal processing, algorithms with O(n) time complexity will cost huge amount of time and that may results in performance degradation of the whole system. A novel multi-step recursive algorithm for variance calculation of the time-varying data series with O(1) time complexity (constant time) is proposed in this paper. Numerical simulation and experiments of the algorithm is presented and the results demonstrate that the proposed multi-step recursive algorithm can effectively decrease computing time and hence significantly improve the variance calculation efficiency for time-varying data, which demonstrates the potential value for time-consumption data analysis or high speed signal processing. [ABSTRACT FROM AUTHOR]

The algorithm complexity of model predictive control (MPC) for cascaded H-bridge (CHB) static synchronous compensators (STATCOMs) was optimized to a polynomial level in previous studies. However, implementing MPC with conventional approaches still suffers from long execution time, where a low cost digital signal processor (DSP) is used to execute optimization algorithms and a small-sized field-programmable gate array (FPGA) is used to extend gate signals and sampling functions. This paper presents a parallel implementation approach to reduce the execution time of MPC, where the FPGA is configured to be used for accelerating the high-complexity sorting tasks. By running the DSP and FPGA in parallel, the algorithm execution time is only determined by the DSP, and the resource consumption is only determined by the FPGA. To minimize the resource consumption and requirement in FPGA, a parallel comparison-based sorter with multiple comparison and accumulators is proposed. The proposed implementation method can reduce the time and space complexity of the MPC from the polynomial level to a linear level without additional hardware cost, which means the MPC for medium-voltage CHB STATCOMs (e.g., 20 stages) can be implemented online with existing control platforms. Experimental results for various CHB STATCOMs are presented to validate the proposed configuration and algorithm. [ABSTRACT FROM AUTHOR]

In this paper we present the algorithm consequences of a model for network expansion that preserves most of the original network properties, notably planarity, cubicity, Hamiltonicity. It is shown that the complexity of the algorithm is linear and the network expansion can be made in real time. [ABSTRACT FROM AUTHOR]

Copyright of Èlektronnoe Modelirovanie is the property of Pukhov Institute for Modeling in Energy Engineering National Academy of Sciences of Ukraine and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Prime numbers are widely used in many fields from engineering to medicine, especially cryptology. The security of cryptographic systems is based on difficult mathematical problems such as the factorization problem used in RSA system. The infinity of prime numbers has been proven but the infinity of twin primes, which is a subset of prime numbers, is still unproven. In this study, an algorithm that finds twin primes smaller than 6a + 1 for any given α e Z+ is proposed. In addition, the proposed algorithm was compared with the sieve of Eratosthenes in terms of performance and memory, and the results were discussed. [ABSTRACT FROM AUTHOR]

Although they are among the most researched real world engineering design problems, it is encountered with significant problems in the optimization of structural truss bar problems (TPs). The main reasons for these problems are (i) the studies on the optimization of TPs being carried out with different experimental settings, (ii) the competitor algorithms used in the optimization process being insufficient, and (iii) the stability analysis and computational complexity information of the algorithms are not investigated. It is designed a simulation environment with defined standards and a benchmarking suite consisting of nine TPs of three different types in order to eliminate these problems. It is found optimum solutions for all problems in the benchmark suite and it is introduced feasible solutions for the first time. According to the statistical analysis results, among the seventy-seven competing algorithms, the best ten algorithms showed competitive performance in the optimization of TPs are LSHADE-EpSin, LSHADE-CnEpSin, SHADE, LSHADE, GSK, FDB-AGDE, MPA, LRFDB-COA and BES. According to the results of the stability analysis carried out on feasible solutions, it has been determined the algorithms with the best success rate for planar type; LSHADE, LSHADE-CnEpSin, LSHADE-EpSin and GSK with 100% success rate, LSHADE-CnEpSin, LSHADE-EpSin, LSHADE and SHADE for Space type with 100% success rate, and LSHADE-EpSin with 69% success rate for frequency constrained type. When the performances of the algorithms are evaluated regardless of the problem type, LSHADE-EpSin has been the most stable algorithm with an overall success rate of 90% on the TPs. Click here for the simulation environment containing the source codes of the ten competitive algorithms and the TP benchmark suite proposed in the article : https://www.mathworks.com/matlabcentral/fileexchange/131668-structural-truss-problems-benchmark-suite. • Feasible solutions for nine different types of truss problems (TPs) were defined in this study for the first time. • LSHADE-CnEpSin, LSHADE-Epsin, LSHADE, SHADE, GSK, BES, FDB-AGDE, MPA and MFLA were applied for the first time for TPs. • The computational complexity and stability of algorithms were presented for the first time. • The results proposed in this article will ensure reusability and widespread impact for future research on TPs. [ABSTRACT FROM AUTHOR]

The present paper analyses a class of nonlinear optimization problems with special restrictions, we propose a direct method for solving the auxiliary problem, for which we calculate complexity, we also assesses the maximum number of elementary operations and describe the optimal algorithm for performing numerical calculations. The study builds an optimal algorithm for solving the auxiliary problem of PG model; the complexity of this algorithm is O(nm2, N), the number of elementary operations is minimal. Matrix inversion does not depend on the size of problem n and always has constant size -m × m, m << n. Thus, the model PG is fully functional and practically “immune” to the size of the optimization problem.

Due to the high computational complexity of massive MIMO system,a low-complexity sparse channel estimation algorithm was proposed utilizing the inherent sparsity of the wireless communication channel to improve the estimation performance.The proposed algorithm separated channel tap from noise space based on the traditional discrete Fourier transform by adopting integral separation algorithm.This channel estimation algorithm need only calculate the channel tap,thus markedly reducing complexity of the algorithm.Numerical simulations show that proposed algorithm can approach to the performance of the minimum mean-square error estimator while maintaining lower complexity.

A third‐order complex delta‐sigma modulation (CDSM) structure with cross‐coupling paths is proposed and analysed. Although the conventional CDSM can reduce circuits complexity in digital transmitter systems, it suffers from other shortcomings like increasing algorithm complexity. This structure imports cross‐coupling paths both at output and interstage, which realises decorrelation between zeros and poles. The advantage is that complex zeros can be arbitrarily placed, and thus, the reconfigurable digital wireless transmitter application can be satisfied; and the poles are not affected by zeros placement, which improves the flatness of signal transfer function. [ABSTRACT FROM AUTHOR]