Time Complexity Of Algorithm Research Articles

Improved space breakdown method - A robust clustering technique for spike sorting.

https://github.com/ArdeleanRichard/Space-Breakdown-Method.

Clustering and analysis of air source heat pump air heater usage patterns of inhabitants in Qinghai-Tibet Plateau areas

Occupant behavior is one of the most important factors influencing the level of energy consumption in the operational phase of buildings. The unique climatic conditions of the Qinghai-Tibetan plateau differ from those of lower altitude areas. Therefore, to specifically investigate the characteristics of the active heating behavior of the inhabitants of these areas, four households are selected for this study. Each is equipped with a corresponding Air Source Heat Pump Air Heater (ASHP-AH) as their only heating equipment. The occupants' usage patterns and active regulating patterns are analyzed explicitly by clustering the ASHP-AH operational data of four households during the heating season using the K-means algorithm. The use of different time steps to reduce the dimensionality of the data and reduce the time and space complexity of the K-means algorithm in clustering is also discussed, and the Preference Cumulative Value (PCV) and Change Direction Frequency (CDF) are proposed to evaluate changes in the clustering results. These results are potentially relevant to improving energy efficiency in relation to occupant behavior.

Optimizing vehicle dynamics co-simulation performance by introducing mesoscopic traffic simulation

Microscopic traffic simulation is often used in conjunction with vehicle dynamics simulation to test cooperative or perception-based driver assistance functions. On the other hand, visualization and the interaction of a large number of swarm vehicles is computationally burdensome, limiting the size of scenarios. To remedy this problem, this paper introduces a mesoscopic traffic model, namely the extension of the shockwave profile model to road networks, that handles traffic as continuous flows of vehicles. Adopting the idea of level of detail from computer graphics, the modeling of swarm vehicles is carried out in less detail farther away from the EGO vehicle. These levels are defined using the classical (macroscopic, mesoscopic, and microscopic) categorization of traffic modeling. The macroscopic traffic model is responsible for the traffic demand and traffic assignment. The proposed mesoscopic model is capable of capturing the fluctuating nature of traffic on lane level. Closer to the EGO vehicle microscopic traffic simulation is employed while the EGO vehicle is modeled in full-detail including vehicle dynamics too. The 3D rendering of the simulation is performed by the vehicle dynamics simulator. The challenge in the proposed methodology is transitioning between the mesoscopic and the microscopic models, i.e., selecting the boundary and spawning/destroying vehicle agents. The paper addresses this challenge with a linear (w.r.t. the vehicle number) time complexity algorithm. Practically, a dynamic downscaling of the microscopic simulation to mesoscopic level is realized outside the vicinity of the EGO vehicle. The proposed methodology is generic, and can be adapted to most existing vehicle dynamics and microscopic traffic simulator software. The solution is tested with SUMO as microsimulation and Carla as vehicle dynamics simulation through a simple path following test case in two scenarios: a congested residential area and a complex scenario with both a highway section and an urban area. Simulation results suggest that the simulation performance could be improved by 200–500% while retaining modeling accuracy, compared to the case when only microscopic simulation is used.

Long-Term Contracts With Dynamic Asymmetric Information for Traffic Offloading in Heterogeneous 5G and Beyond Networks

To achieve a green heterogeneous 5G network, a promising approach is to shut off the light-loaded low-power nodes (LPNs) and transfer the load to the remote radio heads (RRHs) nearby. However, the RRHs may refuse to cooperate when there is no incentive. Considering a user will stay in an RRH for a period of time, how to provide proper long-term incentives for the potential RRHs and select the best one is an essential issue. Since the offloading capability of an RRH is private information, that is, unavailable to the LPNs, in this article, the RRHs’ collaboration incentive problem under such asymmetric information condition is modeled as a long-term contract design problem. In the formulated problem, the channel condition and traffic load, which represent both RRH’s instantaneous state and long-term state, are combined to capture the RRHs’ offloading capacity and used to classify their types. Due to the dynamic of state, an RRH’s type varies with time, which greatly complicates the contract design. We first study the state transition of RRHs and the long-term utilities of both parties, with which the contract-theoretic framework is formulated. Then, we theoretically analyze and simplify the individual rational and incentive-compatible constraints for a feasible long-term contract. Finally, we propose a low time complexity algorithm to find the optimal contract. Numerical results verify that the long-term contract-based incentive mechanism not only improves the utilities of both cooperation parties, but also is superior to the existing works in reducing handover cost and energy consumption.

An improved quantum algorithm for data fitting

As researchers focus on the field of quantum machine learning, there are more and more quantum algorithms for data fitting. However, the majority of quantum algorithms for data fitting are only applicable to sparse matrices, which bring a large number of limitations to their application. In this paper, to solve this problem, we propose a quantum algorithm for data fitting for general matrices, not only sparse and dense matrices. The quantum algorithm is mainly composed of three subroutines which are generating target state, quantum state tomography and estimating fit quality. The time complexity of the quantum algorithm is Oκ4‖A‖Fpolylog(MN)(M′2log(M′)2/ɛ3+1/(ɛϵ2)), where A∈RM×N, κ is the conditional number of matrix A†A∈RN×N, ||A||F is the Frobenius norm of A, M′ is the maxima number of fit functions in allowing fit, ɛ is the fitting error, and ϵ is the error of fit quality estimation. Moreover, our quantum algorithm is independent of the sparsity of the matrix, so our algorithm has wide application in dense matrices and poses a new state of the art for solving dense data fitting.

A Cost-Effective and QoS-Aware User Allocation Approach for Edge Computing Enabled IoT

In edge computing, the app vendors hire resources from edge servers and allocate them to app users to overcome the challenge of the limited computing capacities of their IoT devices. An app vendor intends to provide app services to the maximum number of users with the least number of edge servers in order to make efficient use of edge resources while reducing overall system costs. However, when an edge server has to serve more app users than its capacity, the Quality of Service (QoS) deteriorates. Thus, establishing a tradeoff between cost and QoS is a critical challenge in the process of allocating edge computing resources to users. It is referred to as the app user allocation (AUA) problem. To solve the AUA problem, we propose a distributed game-theoretic approach that finds a pure Nash equilibrium (PNE) as the optimal stable solution. We first model the AUA problem as a constrained optimization problem and then introduce a user allocation game (UAGame) to solve it. This UAGame employs a distributed edge server allocation (ESA) algorithm to reach PNE. The time complexity of the ESA algorithm is reduced by the edge server clustering. It has also been shown that the UAGame is a potential game, and therefore the ESA algorithm is guaranteed to converge at PNE. The performance of the ESA algorithm has also been studied theoretically and validated numerically.

Paw Search – A Searching Approach for Unsorted Data Combining with Binary Search and Merge Sort Algorithm

Searching is one of the oldest core mechanism of nature. Nature is changing gradually along with searching approaches too. Data Mining is one of the most important industrials topic now-a-days. Under this area all social networks, governmental or non-governmental institutions and ecommerce industries produce a huge number of unsorted data and they are to utilize it. For utilizing this huge number of unsorted data there needs some specific features based unsorted data structure tools like searching algorithm. At present there are several sorted data based searching algorithms like Binary Search, Linear Search, Jump Search and Interpolation Search and so on. In this paper of Paw Search Algorithm, it is fully focused to develop a new approach of searching that can work on unsorted data merging several searching techniques and sorting techniques. This algorithm starts its operation by breaking down the given unsorted array into several blocks by making the square root of the length of the given array. Then these blocks will be searched within its specific formula till the target data is found or not, and in the inner side of each block there will be performed Merge Sort and Binary Search approach gradually. Time and Space Complexity of this Paw Search algorithm is comparatively optimal.

Timing-Robust Control over the Cloud Using On-Line Parametric Optimization

In this paper, we present a heuristic method for adapting a networked linear feedback controller to improve its robustness to timing complications, such as long delays, aborted computations, and dropped packets. The core concept of the approach is to log successful sampling and actuation events and then, at discrete time-points, use non-convex parametric optimization to improve the expected performance of the controller under the assumption that the future timing behavior will be similar to the current one. To reduce the time complexity of the optimization algorithm, automatic differentiation is integrated for Efficient gradient descent. The approach is evaluated on a physical ball and beam plant, where both the controller and optimization algorithm can be located in the Cloud.

Network Slicing for NOMA-Enabled Edge Computing

The 5G network presents a new horizon with tremendous opportunities for future generation wireless networks. Mobile edge computing (MEC), non-orthogonal multiple access (NOMA), and network slicing (NS) are some of the key enablers for 5G. MEC reduces the latency to a great extent for a wireless network, while NOMA gives access to more users with resource constraints. NS provides users with a better quality of service and network operators with more flexibility. In this work, we propose an NS technique enabled with NOMA for a MEC network. The proposed NS technique improves service latency for MEC users and reduces the unnecessary allocation of radio resources in NOMA. The saved resources can be leveraged to accommodate more users, thus increasing the spectral efficiency of the network. We consider different types of services based on the task completion time of users in this work. The primary focus is to optimize the total energy consumption for wireless uplink transmission for the NOMA-enabled sliced MEC network. We also propose a heuristic algorithm as an alternative to reduce the time and computational complexities of the optimization algorithm and simulate the results extensively to show the effectiveness of our proposed algorithm.

Efficient computations with counting functions on free groups and free monoids

We present efficient algorithms to decide whether two given counting functions on nonabelian free groups or monoids are at bounded distance from each other and to decide whether two given counting quasimorphisms on nonabelian free groups are cohomologous. We work in the multi-tape Turing machine model with nonconstant-time arithmetic operations. In the case of integer coefficients we construct an algorithm of linear time complexity (assuming that the rank is at least $3$ in the monoid case). In the case of rational coefficients we prove that the time complexity is $O(N\log N)$, where $N$ denotes the size of the input, that is, it is the same as in addition of rational numbers (implemented using the Harvey-van der Hoeven algorithm for integer multiplication). These algorithms are based on our previous work which characterizes bounded counting functions. Bibliography: 20 titles.

Point Cloud Sampling via Graph Balancing and Gershgorin Disc Alignment.

Point cloud (PC)-a collection of discrete geometric samples of a 3D object's surface-is typically large, which entails expensive subsequent operations. Thus, PC sub-sampling is of practical importance. Previous model-based sub-sampling schemes are ad-hoc in design and do not preserve the overall shape sufficiently well, while previous data-driven schemes are trained for specific pre-determined input PC sizes and sub-sampling rates and thus do not generalize well. Leveraging advances in graph sampling, we propose a fast PC sub-sampling algorithm of linear time complexity that chooses a 3D point subset while minimizing a global reconstruction error. Specifically, to articulate a sampling objective, we first assume a super-resolution (SR) method based on feature graph Laplacian regularization (FGLR) that reconstructs the original high-res PC, given points chosen by a sampling matrix H. We prove that minimizing a worst-case SR reconstruction error is equivalent to maximizing the smallest eigenvalue λmin of matrix HT H+ μL, where L is a symmetric, positive semi-definite matrix derived from a neighborhood graph connecting the 3D points. To arrive at a fast algorithm, instead of maximizing λmin, we maximize a lower bound λ-min(HT H+ μL) via selection of H-this translates to a graph sampling problem for a signed graph G with self-loops specified by graph Laplacian L. We tackle this general graph sampling problem in three steps. First, we approximate G with a balanced graph GB specified by Laplacian LB. Second, leveraging a recent linear algebraic theorem called Gershgorin disc perfect alignment (GDPA), we perform a similarity transform Lp = SLB S-1, so that all Gershgorin disc left-ends of Lp are aligned exactly at λmin(LB). Finally, we choose samples on GB using a previous graph sampling algorithm to maximize λ-min(HT H+ μLp) in linear time. Experimental results show that 3D points chosen by our algorithm outperformed competing schemes both numerically and visually in reconstruction quality.

Three-way neighborhood based stream computing for incomplete hybrid information system

Stream computing paradigm focuses on efficiently knowledge updating when immigration and emigration occur simultaneously. Existing stream computing for reasoning with three-way decisions aims at symbolic and complete data. In contrast, the studies on more realistic cases of numerical and symbolic types with potentially incomplete data are preliminary. To efficiently cope with the concept uncertainty, a dynamic neighborhood stream three-way decisions algorithm for incomplete hybrid information systems (DNS3WD) is proposed. Following the setting of flowing into one object and flowing out of another, we dynamically generate all neighborhood classes and decision equivalence classes in the data streaming window. Finally, we deduce the principles of variations of conditional probabilities and update three-way regions accordingly. Theoretically, the time complexity of the non-incremental three-way decisions algorithm (NIH3WD) is about N times that of DNS3WD, where N is the size of the data streaming window. In addition, extensive comparisons against NIH3WD demonstrate that DNS3WD can efficiently leverage the previously acquired knowledge.

Разработка модели оптимизации выбора площадки базовой станции на основе алгоритма PMET-PSO

Existing research in the field of mathematical modeling of base station planning, using intelligent optimization algorithms to solve potential schemes for generating base station distributions, is complex and, for the most part, mathematical models for choosing a base station site require simplification. Also, the existing models for choosing the base station site solve the problem in two-dimensional space and do not take into account the influence of terrain and other factors. Having incorporated the concept of membrane computing into the basis of the MET-PSO algorithm, the PMET-PSO algorithm was developed. The PMET-PSO algorithm is a redesign of the METROPOLIS sample in the simulated annealing algorithm, projects the probability of accepting METROPOLIS in accordance with the number of iterations of the particle swarm algorithm and determines whether to obtain an individual optimal position and a global optimal position generated by a new round of iterations in accordance with probability, thereby adding randomness to the particle swarm algorithm. As the number of iterations increases, the randomness of the particle swarm algorithm decreases, and it converges to an optimal solution. PMET-PSO allows parallel computing, which effectively reduces the time complexity of the MET-PSO algorithm.

An Algorithm of Acoustic Emission Location for Complex Composite Structure

Acoustic emission (AE) is widely used in engineering and rock mechanics. The algorithm of AE location based on homogeneous medium or single velocity structure is confronted with lower accuracy when it is applied to the actual working conditions that are prevailing complicated and heterogeneous. In this paper, an AE location algorithm based on complex composite structure (CCS) is proposed via carrying out the following studies: (1) A new travel time calculation scheme suitable for CCS with step-like velocity change is proposed based on an optimized shortest path algorithm. By doing this, a reasonable ray path that is only deflected at the interface is obtained to improve the travel time accuracy. The time complexity of the new algorithm is O(nlog2n). (2) The availability of the new algorithm is verified via a theoretical analysis under a one-dimensional velocity structure as well as an AE experiment using a complex structure under artificial excitation. (3) The AE location during the failure of a simulated CCS in the laboratory indicates that the new algorithm can effectively calculate the travel time and ray path of the sample.

A New Fuzzy Propagation Model for Influence Maximization in Social Networks

In this paper we introduce a fuzzy propagation model to deal with the influence maximization (IM) problem. The IM problem for the most of existing propagation model is NP-hard. Here, we model social networks as fuzzy directed graphs to propose an application-oriented propagation process. To this aim, we investigate an interesting relationship between zero forcing set concept in graphs and IM problem in social networks. In spite of its attractive theory, its implementation is not efficient in the real world. Thus, we improve the fuzzy zero forcing set concept and suggest our fuzzy propagation model, simultaneously. Moreover, we present a polynomial time complexity algorithm to solve IM problems under the proposed propagation process. In particular, we consider a propagation parameter to control the size of the seed set and its coverage. Also, experimental results on some real world social networks show that the propagation model finds optimal and flexible seed set.

Certification of an exact worst-case self-stabilization time

Unlike qualitative properties such as correctness (safety and liveness), quantitative properties of distributed algorithms have only been certified in very few studies. This work is the first attempt to certify time complexity bounds of a fault-tolerant distributed algorithm. Our case study consists in formally proving, using the Coq proof assistant, the time complexity of the first Dijkstra's self-stabilizing token ring algorithm. In more detail, we formally prove both the self-stabilization and exact worst-case stabilization time of this algorithm assuming asynchronous settings. This latter result is obtained in two main steps. First, we certify a non-trivial upper bound on the stabilization time, i.e., every execution in an N-size ring contains at most 3⋅N⋅(N−1)2−N−1 steps if N≥4, at most 3 steps if N=3; and in remaining cases, the stabilization time is zero. Then, for each case, we exhibit a possible execution whose complexity exactly matches those upper bounds. Notice that the tight bounds for N=3 and N≥4 were unknown until now, even among self-stabilization researchers.

Deterministic non-adaptive contention resolution on a shared channel

In a multiple access channel, autonomous stations are able to transmit and listen to a shared device. A fundamental problem, called contention resolution, is to allow any station to successfully deliver its message by resolving the conflicts that arise when several stations transmit simultaneously. Despite a long history on such a problem, most of the results deal with the static setting when all stations start simultaneously, while many fundamental questions remain open in the realistic scenario when stations can join the channel at arbitrary times. In this paper, we explore the impact that three major channel features (asynchrony among stations, knowledge of the number of contenders and possibility of switching off stations after a successful transmission) can have on the time complexity of non-adaptive deterministic algorithms. We establish upper and lower bounds allowing to understand which parameters permit time-efficient contention resolution and which do not.

Power system abnormal pattern detection for new energy big data

Abstract The energy crisis is a problem that countries all over the world pay more and more attention to, and a series of ecological problems caused by it have become increasingly prominent. It is difficult for traditional fossil fuels to maintain a healthy and coordinated sustainable development of society and economy. The establishment of a sustainable energy system has become the development trend of various countries to solve energy problems. Electric energy is a secondary energy that all primary energy can be converted into, and an irreplaceable consumable for all industrial technologies and people’s lives. Electric power data has the characteristics of large rate span, numerous data sources, complicated interaction methods, and various types of data. The existence of abnormal data in the power system will greatly reduce the accuracy of the system state estimation and the state estimation convergence rate. This paper introduces the power grid industrial control system, combines the data flow of power big data, and analyzes the abnormal information detection process in detail. It takes the data stream acquired by the acquisition unit PMU of the wide area measurement system as the research object. The rapid development of the Hadoop big data platform provides important technical support for the research of power grid big data. Based on the Hadoop platform, the clustering algorithm is used to complete the anomaly detection of real-time data. The LOF algorithm has poor performance when dealing with a large amount of high-dimensional data, and has high time and space complexity. In order to make up for the shortcomings of the LOF algorithm, this paper uses the K-means clustering algorithm to propose an improved algorithm K-LOF of the density-based local abnormal factor detection algorithm LOF, and optimizes the neighborhood query process. It is verified by experiments that the K-LOF algorithm can effectively reduce the time complexity of the anomaly detection algorithm and improve the detection accuracy by 2–4.2%.

A Segmented PageRank-Based Value Compensation Method for Personal Data in Alliance Blockchains

Alliance blockchains provide a multi-party trusted data trading environment, promoting the development of the data trading market in which the value compensation for personal data is still a key issue. However, limited by the data format and content, traditional attempts on data value compensation cannot form a widely applicable solution. Therefore, we propose a universal value compensation method for personal data in alliance blockchains. The basic idea of this method is to evaluate the value weight of data based on the collaborative relationship of data value. First, we construct a Data Collaboration Markov Model (DCMM) to formalize the collaboration network of data value. Then, aiming at data collaboration networks with different structures, the corresponding Segmented PageRank (SPR) algorithm is proposed. SPR can universally evaluate the value weight of each data account without being subjected to the data format or content. Finally, we theoretically deduce that the time complexity and space complexity of SPR algorithm are respectively 1 / K and 1 / K 2 taken by PageRank algorithm. Experiments show the feasibility and superior performance of SPR.

Case report: Quantitative recognition of virtual human technology acceptance based on efficient deep neural network algorithm.

With the advancement of artificial intelligence, robotics education has been a significant way to enhance students' digital competency. In turn, the willingness of teachers to embrace robotics education is related to the effectiveness of robotics education implementation and the sustainability of robotics education. Two hundred and sixty-nine teachers who participated in the "virtual human education in primary and secondary schools in Guangdong and Henan" and the questionnaire were used as the subjects of study. UTAUT model and its corresponding scale were modified by deep learning algorithms to investigate and analyze teachers' acceptance of robotics education in four dimensions: performance expectations, effort expectations, community influence and enabling conditions. Findings show that 53.68% of the teachers were progressively exposed to robotics education in the last three years, which is related to the context of the rise of robotics education in schooling in recent years, where contributing conditions have a direct and significant impact on teachers' acceptance of robotics education. The correlation coefficients between teacher performance expectations, effort expectations, community influence, and enabling conditions and acceptance were 0.290 (p = 0.000<0.001), -0.144 (p = 0.048<0.05), 0.396 (p = 0.000<0.001), and 0.422 (p = 0.000<0.001) respectively, indicating that these four core dimensions both had a significant effect on acceptance. Optimization comparison results of deep learning models show that mDAE and AmDAE provide a substantial reduction in training time compared to existing noise-reducing autoencoder models. It is shown that time-complexity of the deep neural network algorithm is positively related to the number of layers of the model.