Time Complexity Of Algorithm Research Articles

A New Framework for Hierarchical Drawings

We present a new approach to visualize directed graphs and their hierarchies that departs from the classical four-phase framework of Sugiyama and computes readable hierarchical visualizations that focus on the reachability information of a directed acyclic graph. Additionally, our approach has the feature that a few transitive edges are not drawn in the drawing, thus reducing the visual complexity of the resulting drawing. Furthermore, the problems involved in our framework require only polynomial time. The channel decomposition is a partition of the vertex set of the graph into channels, where a channel is a relaxed path. Our framework offers a suite of solutions depending upon the requirements, and it consists of only two steps: (a) the cycle removal step (if the directed graph contains cycles) and (b) the channel decomposition and hierarchical drawing step. Our framework does not introduce any dummy vertices and it keeps the vertices of a path/channel vertically aligned. The time complexity of the main drawing algorithms of our framework is $O(km)$, where $k$ is the number of paths/channels, typically much smaller than $n$ (the number of vertices).

An adaptive greedy flow routing algorithm for performance improvement in software‐defined network

AbstractThe software‐defined network (SDN) is an architecture to separate control and data plane. There is a central controller to control the forwarding elements (FEs) under its domain. The controller can receive flows information and requirements to make a decision and impose rules to FEs for forwarding all packets belong to each flow. Routing can be done with considering performance parameters that are needed for each flow. The routing algorithms that support the thresholds of the flows' bandwidth, delay, jitter, and packet loss rate (PLR) are needed in the SDN architecture to optimize the delay, the blocking probability (BP), and the network utilization with an acceptable algorithm running time. In this paper, we proposed the greedy routing scheme in the Floodlight controller and evaluated this algorithm with the utilization, delay, BP, and algorithm time complexity. Extensive simulations are performed, and achieved results confirm the effectiveness of the proposed scheme in comparison with other baseline routing protocols such as random, shortest path (SP), and adaptive flow routing (AFR).

Novel Image Segmentation Methods Based on Improved Ncut Algorithm

Image segmentation is an important process from image processing to image analysis and scene understanding. Targets of different scales in an image may belong to different classes. Single scale image segmentation methods are prone to over-segmentation or under-segmentation. Combining MeanShfit and Ncut multiscale sampling image segmentation methods, the image is smoothed by MeanShift algorithm and the edges are preserved. Clustering using weights (similarities) between two pixels by Ncut method, this method can be applied to remote sensing image segmentation. In order to solve the problems of high time complexity and long calculation time of Ncut algorithm, firstly, the entropy rate superpixel segmentation algorithm is used to over-segment the image. The algorithm divides the image into a series of compact regions with good regional consistency, Combining Ncut method to solve the weights of similarity between two superpixels to determine the attribution of the region can reduce the segmentation time. Experiments show that this method can use multiscale information for image segmentation effectively. The first method can be applied to remote sensing image segmentation, and the second method can improve the efficiency of Ncut which is suitable for natural scene image segmentation.

A novel strong tracking cubature Kalman filter and its application in maneuvering target tracking

The fading factor exerts a significant role in the strong tracking idea. However, traditional fading factor introduction method hinders the accuracy and robustness advantages of current strong-tracking-based nonlinear filtering algorithms such as Cubature Kalman Filter (CKF) since traditional fading factor introduction method only considers the first-order Taylor expansion. To this end, a new fading factor idea is suggested and introduced into the strong tracking CKF method. The new fading factor introduction method expanded the number of fading factors from one to two with reselected introduction positions. The relationship between the two fading factors as well as the general calculation method can be derived based on Taylor expansion. Obvious superiority of the newly suggested fading factor introduction method is demonstrated according to different nonlinearity of the measurement function. Equivalent calculation method can also be established while applied to CKF. Theoretical analysis shows that the strong tracking CKF can extract the third-order term information from the residual and thus realize second-order accuracy. After optimizing the strong tracking algorithm process, a Fast Strong Tracking CKF (FSTCKF) is finally established. Two simulation examples show that the novel FSTCKF improves the robustness of traditional CKF while minimizing the algorithm time complexity under various conditions.

A Modified KNN Indoor WiFi Localization Method With K-median Cluster

Because of the serious attenuation and multi-path effect of GPS signal, outdoor-positioning technology can not be applied in complex indoor environment. Through the study of K-Nearest Neighbor applied in WiFi positioning, according to the problem that the time complexity of KNN algorithm increases linearly with the quantity of samples, this paper combined clustering algorithm with KNN optimized the similarity measure in fingerprint feature space and proposed a efficient indoor target location algorithm . Experimental results showed that the algorithm improved the positioning accuracy, had strong robustness to noise and more importantly, the positioning time was effectively shortened and it can meet the requirements of practical applications.

Fuzzy clustering and fuzzy c-means partition cluster analysis and validation studies on a subset of citescore dataset

A hard partition clustering algorithm assigns equally distant points to one of the clusters, where each datum has the probability to appear in simultaneous assignment to further clusters. The fuzzy cluster analysis assigns membership coefficients of data points which are equidistant between two clusters so the information directs have a place toward in excess of one cluster in the meantime. For a subset of CiteScore dataset, fuzzy clustering (fanny) and fuzzy c-means (fcm) algorithms were implemented to study the data points that lie equally distant from each other. Before analysis, clusterability of the dataset was evaluated with Hopkins statistic which resulted in 0.4371, a value < 0.5, indicating that the data is highly clusterable. The optimal clusters were determined using NbClust package, where it is evidenced that 9 various indices proposed 3 cluster solutions as best clusters. Further, appropriate value of fuzziness parameter <em>m</em> was evaluated to determine the distribution of membership values with variation in <em>m</em> from 1 to 2. Coefficient of variation (CV), also known as relative variability was evaluated to study the spread of data. The time complexity of fuzzy clustering (fanny) and fuzzy c-means algorithms were evaluated by keeping data points constant and varying number of clusters.

Staggered parallel short-time Fourier transform

In this paper, we present the staggered parallel short-time Fourier transform, an algorithm that uses a quasi-parallel procedure to compute exact STFT coefficients of 1D signals. The algorithm leverages parallelism with the capacity of feedforward STFT algorithms to re-use prior computations. It performs this by carefully organizing input signals and collecting past computations into 2D memory buffers. Re-using stored information in memory enables fast computation of up to N/2 FFTs in parallel. The algorithm's time complexity is at O[6T] under an abstract circuit implementation – achieving a complexity measure that is independent of sample complexity N. Its time complexity is asymptotically equivalent with the best possible exact algorithm of O[T] time complexity, with a constant efficiency at O[1] relative to the best known sequential algorithm. Its efficiency property holds whether in an abstract circuit implementation or in a CPU implementation with limited number of cores. In general, the algorithm consumes less processors than other parallel STFT algorithms but can potentially require more memory. To test the algorithm's properties, we implement several STFT algorithms in a CPU with varying numbers of cores. These algorithms use either FFT, iterative, or feedforward schemes to capture the range of existing STFT algorithms for comparison. From our experimental results, our proposed algorithm has the least running time among exact STFT algorithms, while consuming less CPU processors than other forms of parallel implementations.

SmartStreamer: Preference-Aware Multipath Video Streaming Over MPTCP

Simultaneous access to multiple interfaces (e.g., WiFi and cellular networks) can significantly improve the users’ quality of experience (QoE) in video streaming. However, some interfaces could be more expensive to use and less energy efficient. Therefore, in this paper, we propose a preference-aware multipath video streaming algorithm over HTTP using multipath TCP (MPTCP). First, we formulate the quality decisions of the video chunks and the chunk's download policy subject to the chunk's deadlines, the available bandwidth of the different paths, and the link preferences as a non-convex optimization problem. The objective is to optimize a novel QoE metric that maintains a tradeoff between maximizing the quality of every video's chunk and ensuring quality fairness among all chunks for the minimum re-buffering (stall) duration, and without violating the link preference constraint. Second, we develop a polynomial time complexity algorithm to solve the proposed optimization problem, and provide guarantees for the proposed algorithm. We further propose a sliding window based online algorithm where several challenges including short bandwidth prediction with prediction errors are addressed. Extensive emulated experiments with real bandwidth traces of public datasets reveal the robustness of our scheme and demonstrate its significant performance improvement compared to the state-of-the-art multi-path streaming algorithms.

Eavesdropping-Aware Routing and Spectrum/Code Allocation in OFDM-Based EONs Using Spread Spectrum Techniques

In this work, eavesdropping-aware routing and spectrum/code allocation techniques are proposed for elastic optical networks (EONs) using orthogonal frequency division multiplexing (OFDM). To introduce physical (optical) layer security and protect these networks against eavesdropping attacks, spread spectrum (SS) with signal overlapping techniques are used to encode each requested confidential connection. In order to make sense of accessed information and compromise a confidential connection, an eavesdropper will now have to lock on the correct frequency, determine the correct code and symbol sequence among co-propagated overlapped signals, and decode the signal. Different novel policies are presented for the assignment of spectrum and the codes for each confidential demand along with different routing strategies, resulting in an extra layer of security for confidential demands. Depending on the spectrum/code allocation and routing policies utilized, different (extra) levels of security are added for confidential connections while also considering the spectrum utilization, the blocking rate, and the algorithmic time complexity required for connection provisioning.

A signal-diffusion-based spectral clustering method for community detection

As the traditional spectral community detection method uses adjacency matrix for clustering which might cause the problem of accuracy reduction, we proposed a signal-diffusion-based spectral clustering for community detection. This method solves the problem that unfixed total signal as using the signal transmission mechanism, provides optimization of algorithm time complexity, improves the performance of spectral clustering with construction of Laplacian based on signal diffusion. Experiments prove that the method reaches as better performance on real-world network and Lancichinetti–Fortunato–Radicchi (LFR) benchmark.

Markov chain‐based wind power time series modelling method considering the influence of the state duration on the state transition probability

Due to the inherent uncertainties of wind power, its large-scale integration strongly impacts the planning and operation of power systems. To investigate these impacts, a stochastic model is required to more accurately capture the wind power's characteristics. This study proposes an improved Markov chain (MC)-based time series (TS) modelling method for the stochastic generation of synthetic wind power TS. First, a self-adaptive state division strategy is proposed to objectively classify historical data into several typical states. This strategy combines a state optimisation clustering model with a random-variable-modelling-oriented filter parameter optimisation method. Then, a three-dimensional state transition probability matrix (STPM) is proposed and constructed to generate synthetic wind power state TS. In contrast to the previous STPMs, the proposed STPM can capture the changing pattern of the transition probability against the state duration. Finally, the fluctuation quantity and noise are separately and sequentially added to the generated state TS, as an improvement over previous fluctuation characteristic addition methods, to obtain the final synthetic wind power TS. The results show that the proposed method outperforms previous MC-based TS modelling methods in reproducing historical characteristics, such as the transition and fluctuation characteristics, and does not increase the STPM construction algorithm's time complexity.

Approximating constrained minimum cost input–output selection for generic arbitrary pole placement in structured systems

This paper deals with minimum cost constrained selection of inputs, outputs and feedback pattern in structured systems, referred to as optimal input–output and feedback co-design problem. The input–output set is constrained in the sense that the set of states that each input can influence and the set of states that each output can sense are pre-specified. Further, each input and each output are associated with a cost. The feedback pattern is unconstrained and the cost of a feedback edge is the sum of cost of the input and output associated with it. Our goal is to optimally select an input–output set and a feedback pattern such that the closed-loop system has no structurally fixed modes (SFMs). This problem is known to be NP-hard. In this paper, we show that the problem is inapproximable to factor (1−o(1))logn, where n denotes the number of states in the system. Then we present an approximation algorithm of time complexity O(n3) to approximate the problem. We prove that the proposed algorithm gives a (2logn)-approximate solution to the problem. Thus the algorithm given in this paper is an order optimal approximation algorithm to approximate the optimal input–output and feedback co-design problem.

Reduction algorithm based on finding the maximum mutual information in incomplete information systems

Aiming at such drawbacks of the existing incomplete information system attribute reduction algorithms as high time complexity and insufficiency of the reduction result completeness, this paper proposes an attribute reduction algorithm based on finding the maximum mutual information via weakening the equivalence class in classical rough set theory into tolerance class and through combining the definition of information entropy with the tolerance class. Taking the mutual information of condition attribute and decision attribute as the iterative criterion, and the empty set as the initial reduction, the algorithm superposes the condition attribute set corresponding to the maximum value of the mutual information of condition attributes and decision attributes, thus equating the mutual information of condition attribute set and decision attribute with the information entropy of decision attribute, obtaining the relative reduction of the incomplete decision system and guaranteeing the completeness of the reduction result. In the solution of the attribute set tolerance class, an algorithm with lower time complexity is adopted, which can reduce the time complexity of the whole algorithm. The feasibility of the algorithm is illustrated by an example.

On the quantum adiabatic evolution with the most general system Hamiltonian

In this paper, we study the problem that when quantum adiabatic evolution with the most general form of system Hamiltonian will get failed. Here the most general form means that the initial and final Hamiltonians are just designed according to the adiabatic theorem in quantum mechanics. As we will see, even in this most general model of quantum adiabatic evolution, it still exists the possibility that the quantum adiabatic computation can fail totally if some condition is satisfied, which implies the time complexity of the quantum algorithm is infinity. That is, here we propose a rather general criterion for judging whether a quantum adiabatic evolution is successful. This result largely extends the authors’ previous research on this topic, and it may be seen as a further important clue for us when designing quantum algorithms in the framework of adiabatic evolution for some practical problems.

Improved Weighted Page Ranking Algorithm Based on Principal Component Analysis and Map Reduce Frame work for Web Access

In general the World Wide Web become the most useful information resource used for information retrievals and knowledge discoveries. But the Information on Web to be expand in size and density. The retrieval of the required information on the web is efficiently and effectively to be challenge one. For the tremendous growth of the web has created challenges for the search engine technology. Web mining is an area in which applies data mining techniques to deal the requirements. The following are the popular Web Mining algorithms, such as PageRanking (PR), Weighted PageRanking (WPR) and Hyperlink-Induced Topic Search (HITS), are quite commonly used algorithm to sort out and rank the search results. In among the page ranking algorithm uses web structure mining and web content mining to estimate the relevancy of a web site and not to deal the scalability problem and also visits of inlinks and outlinks of the pages. In recent days to access fast and efficient page ranking algorithm for webpage retrieval remains as a challenging. This paper proposed a new improved WPR algorithm which uses a Principal Component Analysis technique called (PWPR) based on mean value of page ranks. The proposed PWPR algorithm takes into account the importance of both the number of visits of inlinks and outlinks of the pages and distributes rank scores based on the popularity of the pages. The weight values of the pages is computed from the inlinks and outlinks with their mean values. But in PWPR method new data and updates are constantly arriving, the results of data mining applications become stale and obsolete over time. To solve this problem is a MapReduce (MR) framework is promising approach to refreshing mining results for mining big data .The proposed MR algorithm reduces the time complexity of the PWPR algorithm by reducing the number of iterations to reach a convergence point.

Improving Time Complexity and Accuracy of the Machine Learning Algorithms Through Selection of Highly Weighted Top k Features from Complex Datasets

Machine learning algorithms (MLAs) usually process large and complex datasets containing a substantial number of features to extract meaningful information about the target concept (a.k.a class). In most cases, MLAs suffer from the latency and computational complexity issues while processing such complex datasets due to the presence of lesser weight (i.e., irrelevant or redundant) features. The computing time of the MLAs increases explosively with increase in the number of features, feature dependence, number of records, types of the features, and nested features categories present in such datasets. Appropriate feature selection before applying MLA is a handy solution to effectively resolve the computing speed and accuracy trade-off while processing large and complex datasets. However, selection of the features that are sufficient, necessary, and are highly co-related with the target concept is very challenging. This paper presents an efficient feature selection algorithm based on random forest to improve the performance of the MLAs without sacrificing the guarantees on the accuracy while processing the large and complex datasets. The proposed feature selection algorithm yields unique features that are closely related with the target concept (i.e., class). The proposed algorithm significantly reduces the computing time of the MLAs without degrading the accuracy much while learning the target concept from the large and complex datasets. The simulation results fortify the efficacy and effectiveness of the proposed algorithm.

QCF: Quantum Collaborative Filtering Recommendation Algorithm

With the rapid development of the Internet, e-commerce plays an important role in people’s lives, and the recommendation system is one of the most critical technologies. However, as the number of users and the scale of goods increase sharply, the traditional collaborative filtering recommendation algorithm has a large computational complexity in the part of calculating the user similarity, which leads to a low recommendation efficiency. In response to the above problems, this paper introduces the concept of quantum computing theory. The user score vector is first prepared into a quantum state, the similarity score is calculated in parallel, then the similarity information is saved into the quantum bit, and finally the similar user is searched by the Grover search algorithm. Compared with the traditional collaborative filtering recommendation algorithm, the time complexity of the collaborative filtering recommendation algorithm based on Grover algorithm can be effectively reduced under certain conditions.

Комплементарний аналіз використання потенціалу та можливостей відкритих он-лайн курсів у процесі вивчення дисципліни “Алгоритми та структура даних”

The article is devoted to the analysis of the potential of the use of mass open online courses in the study of the discipline "Algorithms and data structures" in the process of training engineers-programmers and engineers-teachers in the specialty 122 "Computer Science". and 015.10 Vocational education (computer technology) in higher education institutions. Comparatively massive open online courses for the study of algorithms, in particular, Codecademy specialization "Data Structures and Algorithms", course EdX "Algorithms" and course Prometheus "Development and Analysis of Algorithms." The didactic possibilities of using MOOC Prometheus "Development and analysis of algorithms" in the course of studying the discipline "Algorithms and data structures" as additional material are discussed. The use of MOOC as an additional resource of Prometheus and the course "Development and analysis of algorithms" in the course of studying the discipline "Algorithms and Data Structure" in the training of future engineers-programmers will help form competencies such as: knowledge and skills to use the basic algorithms and data structures, the basic concepts of theoretical algorithms, computational issues, solvability and insolubility of mass problems, concepts of time and spatial complexity of algorithms in solving computational problems. It is concluded that the use of mass open online courses on discipline "Algorithms and data structure". At present, it is better to use MOOC as additional learning resources for students and teachers. Introducing these courses as an alternative or complement to individual parts of the training material has certain perspectives. This will diversify the learning process, deepen the knowledge of discipline and consider the practical implementation of algorithms. Keywords: mass open on-line course, program engineers, algorithms and data structure, resource, algorithms on graphs, data structure, algorithms.

Fast kernel extreme learning machine for ordinal regression

Ordinal regression is a special kind of machine learning problem, which aims to label patterns with an ordinal scale. Due to the ubiquitous existence of the ordering information in many practical cases, ordinal regression has received much attention and can be found in a great variety of applications. Meanwhile, Kernel Extreme Learning Machine (KELM), as the extension of Extreme Learning Machine in the framework of kernel learning, has shown its strength in many machine learning tasks. Nevertheless, existing KELM methods have paid little attention to ordinal regression especially in large-scale situations. In this paper, we consider the kernel technique and ordinal scales in labels at the same time, and propose a new KELM model for ordinal regression by exploiting a quadratic cost-sensitive encoding scheme. In order to make the training process more efficient in the big data scenario, a fast algorithm is designed based on the low rank approximation. The incomplete Cholesky factorization and the Sherman–Morrison–Woodbury formula are utilized together to avoid computing the inverse of the kernel matrix. The time complexity of the new algorithm is thus linear with the number of the training instances, which makes it suitable to the large-scale occasions. Numerical experiments on multiple public datasets validate the effectiveness and efficiency of the proposed methods.

A new statistic for efficient detection of repetitive sequences.

Detecting sequences containing repetitive regions is a basic bioinformatics task with many applications. Several methods have been developed for various types of repeat detection tasks. An efficient generic method for detecting most types of repetitive sequences is still desirable. Inspired by the excellent properties and successful applications of the D2 family of statistics in comparative analyses of genomic sequences, we developed a new statistic D2R that can efficiently discriminate sequences with or without repetitive regions. Using the statistic, we developed an algorithm of linear time and space complexity for detecting most types of repetitive sequences in multiple scenarios, including finding candidate clustered regularly interspaced short palindromic repeats regions from bacterial genomic or metagenomics sequences. Simulation and real data experiments show that the method works well on both assembled sequences and unassembled short reads. The codes are available at https://github.com/XuegongLab/D2R_codes under GPL 3.0 license. Supplementary data are available at Bioinformatics online.