Showing papers on "Time complexity published in 2021"

TEASER: Fast and Certifiable Point Cloud Registration

Abstract: We propose the first fast and certifiable algorithm for the registration of two sets of three-dimensional (3-D) points in the presence of large amounts of outlier correspondences. A certifiable algorithm is one that attempts to solve an intractable optimization problem (e.g., robust estimation with outliers) and provides readily checkable conditions to verify if the returned solution is optimal (e.g., if the algorithm produced the most accurate estimate in the face of outliers) or bound its suboptimality or accuracy. Toward this goal, we first reformulate the registration problem using a truncated least squares (TLS) cost that makes the estimation insensitive to a large fraction of spurious correspondences. Then, we provide a general graph-theoretic framework to decouple scale, rotation, and translation estimation, which allows solving in cascade for the three transformations. Despite the fact that each subproblem (scale, rotation, and translation estimation) is still nonconvex and combinatorial in nature, we show that 1) TLS scale and (component-wise) translation estimation can be solved in polynomial time via an adaptive voting scheme, 2) TLS rotation estimation can be relaxed to a semidefinite program (SDP) and the relaxation is tight, even in the presence of extreme outlier rates, and 3) the graph-theoretic framework allows drastic pruning of outliers by finding the maximum clique. We name the resulting algorithm TEASER ( Truncated least squares Estimation And SEmidefinite Relaxation ). While solving large SDP relaxations is typically slow, we develop a second fast and certifiable algorithm, named TEASER++, that uses graduated nonconvexity to solve the rotation subproblem and leverages Douglas-Rachford Splitting to efficiently certify global optimality. For both algorithms, we provide theoretical bounds on the estimation errors, which are the first of their kind for robust registration problems. Moreover, we test their performance on standard benchmarks, object detection datasets, and the 3DMatch scan matching dataset, and show that 1) both algorithms dominate the state-of-the-art (e.g., RANSAC, branch-&-bound, heuristics) and are robust to more than $\text{99}\%$ outliers when the scale is known, 2) TEASER++ can run in milliseconds and it is currently the fastest robust registration algorithm, and 3) TEASER++ is so robust it can also solve problems without correspondences (e.g., hypothesizing all-to-all correspondences), where it largely outperforms ICP and it is more accurate than Go-ICP while being orders of magnitude faster. We release a fast open-source C++ implementation of TEASER++.

CrossViT: Cross-Attention Multi-Scale Vision Transformer for Image Classification

Abstract: The recently developed vision transformer (ViT) has achieved promising results on image classification compared to convolutional neural networks. Inspired by this, in this paper, we study how to learn multi-scale feature representations in transformer models for image classification. To this end, we propose a dual-branch transformer to combine image patches (i.e., tokens in a transformer) of different sizes to produce stronger image features. Our approach processes small-patch and large-patch tokens with two separate branches of different computational complexity and these tokens are then fused purely by attention multiple times to complement each other. Furthermore, to reduce computation, we develop a simple yet effective token fusion module based on cross attention, which uses a single token for each branch as a query to exchange information with other branches. Our proposed cross-attention only requires linear time for both computational and memory complexity instead of quadratic time otherwise. Extensive experiments demonstrate that our approach performs better than or on par with several concurrent works on vision transformer, in addition to efficient CNN models. For example, on the ImageNet1K dataset, with some architectural changes, our approach outperforms the recent DeiT by a large margin of 2\% with a small to moderate increase in FLOPs and model parameters. Our source codes and models are available at \url{this https URL}.

Lite-HRNet: A Lightweight High-Resolution Network

Abstract: We present an efficient high-resolution network, Lite-HRNet, for human pose estimation. We start by simply applying the efficient shuffle block in ShuffleNet to HRNet (high-resolution network), yielding stronger performance over popular lightweight networks, such as MobileNet, ShuffleNet, and Small HRNet. We find that the heavily-used pointwise (1 × 1) convolutions in shuffle blocks become the computational bottleneck. We introduce a lightweight unit, conditional channel weighting, to replace costly pointwise (1 × 1) convolutions in shuffle blocks. The complexity of channel weighting is linear w.r.t the number of channels and lower than the quadratic time complexity for pointwise convolutions. Our solution learns the weights from all the channels and over multiple resolutions that are readily available in the parallel branches in HRNet. It uses the weights as the bridge to exchange information across channels and resolutions, compensating the role played by the pointwise (1 × 1) convolution. Lite-HRNet demonstrates superior results on human pose estimation over popular lightweight networks. Moreover, Lite-HRNet can be easily applied to semantic segmentation task in the same lightweight manner. The code and models have been publicly available at https://github.com/HRNet/Lite-HRNet.

Integer multiplication in time O(n log n)

Abstract: We present an algorithm that computes the product of two n-bit integers in O(n log n) bit operations, thus confirming a conjecture of Schonhage and Strassen from 1971. Our complexity analysis takes place in the multitape Turing machine model, with integers encoded in the usual binary representa- tion. Central to the new algorithm is a novel “Gaussian resampling” technique that enables us to reduce the integer multiplication problem to a collection of multidimensional discrete Fourier transforms over the complex numbers, whose dimensions are all powers of two. These transforms may then be evaluated rapidly by means of Nussbaumer’s fast polynomial transforms.

A Novel K-Means Clustering Algorithm with a Noise Algorithm for Capturing Urban Hotspots

Abstract: With the development of cities, urban congestion is nearly an unavoidable problem for almost every large-scale city. Road planning is an effective means to alleviate urban congestion, which is a classical non-deterministic polynomial time (NP) hard problem, and has become an important research hotspot in recent years. A K-means clustering algorithm is an iterative clustering analysis algorithm that has been regarded as an effective means to solve urban road planning problems by scholars for the past several decades; however, it is very difficult to determine the number of clusters and sensitively initialize the center cluster. In order to solve these problems, a novel K-means clustering algorithm based on a noise algorithm is developed to capture urban hotspots in this paper. The noise algorithm is employed to randomly enhance the attribution of data points and output results of clustering by adding noise judgment in order to automatically obtain the number of clusters for the given data and initialize the center cluster. Four unsupervised evaluation indexes, namely, DB, PBM, SC, and SSE, are directly used to evaluate and analyze the clustering results, and a nonparametric Wilcoxon statistical analysis method is employed to verify the distribution states and differences between clustering results. Finally, five taxi GPS datasets from Aracaju (Brazil), San Francisco (USA), Rome (Italy), Chongqing (China), and Beijing (China) are selected to test and verify the effectiveness of the proposed noise K-means clustering algorithm by comparing the algorithm with fuzzy C-means, K-means, and K-means plus approaches. The compared experiment results show that the noise algorithm can reasonably obtain the number of clusters and initialize the center cluster, and the proposed noise K-means clustering algorithm demonstrates better clustering performance and accurately obtains clustering results, as well as effectively capturing urban hotspots.

Mixup for Node and Graph Classification

Abstract: Mixup is an advanced data augmentation method for training neural network based image classifiers, which interpolates both features and labels of a pair of images to produce synthetic samples. However, devising the Mixup methods for graph learning is challenging due to the irregularity and connectivity of graph data. In this paper, we propose the Mixup methods for two fundamental tasks in graph learning: node and graph classification. To interpolate the irregular graph topology, we propose the two-branch graph convolution to mix the receptive field subgraphs for the paired nodes. Mixup on different node pairs can interfere with the mixed features for each other due to the connectivity between nodes. To block this interference, we propose the two-stage Mixup framework, which uses each node’s neighbors’ representations before Mixup for graph convolutions. For graph classification, we interpolate complex and diverse graphs in the semantic space. Qualitatively, our Mixup methods enable GNNs to learn more discriminative features and reduce over-fitting. Quantitative results show that our method yields consistent gains in terms of test accuracy and F1-micro scores on standard datasets, for both node and graph classification. Overall, our method effectively regularizes popular graph neural networks for better generalization without increasing their time complexity.

Minimum cost flows, MDPs, and ℓ1-regression in nearly linear time for dense instances

Abstract: In this paper we provide new randomized algorithms with improved runtimes for solving linear programs with two-sided constraints. In the special case of the minimum cost flow problem on n-vertex m-edge graphs with integer polynomially-bounded costs and capacities we obtain a randomized method which solves the problem in O(m + n1.5) time. This improves upon the previous best runtime of O(m √n) [Lee-Sidford’14] and, in the special case of unit-capacity maximum flow, improves upon the previous best runtimes of m4/3 + o(1) [Liu-Sidford’20, Kathuria’20] and O(m √n) [Lee-Sidford’14] for sufficiently dense graphs. In the case of l1-regression in a matrix with n-columns and m-rows we obtain a randomized method which computes an є-approximate solution in O(mn + n2.5) time. This yields a randomized method which computes an є-optimal policy of a discounted Markov Decision Process with S states and, A actions per state in time O(S2 A + S2.5). These methods improve upon the previous best runtimes of methods which depend polylogarithmically on problem parameters, which were O(mn1.5) [Lee-Sidford’15] and O(S2.5 A) [Lee-Sidford’14, Sidford-Wang-Wu-Ye’18] respectively. To obtain this result we introduce two new algorithmic tools of possible independent interest. First, we design a new general interior point method for solving linear programs with two sided constraints which combines techniques from [Lee-Song-Zhang’19, Brand et al.’20] to obtain a robust stochastic method with iteration count nearly the square root of the smaller dimension. Second, to implement this method we provide dynamic data structures for efficiently maintaining approximations to variants of Lewis-weights, a fundamental importance measure for matrices which generalize leverage scores and effective resistances.

Training Variational Quantum Algorithms Is NP-Hard.

Abstract: Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum approximate optimization algorithms that solve ground state problems from quantum chemistry and binary optimization problems, respectively. They are based on the idea of using a classical computer to train a parametrized quantum circuit. We show that the corresponding classical optimization problems are NP-hard. Moreover, the hardness is robust in the sense that, for every polynomial time algorithm, there are instances for which the relative error resulting from the classical optimization problem can be arbitrarily large assuming that P≠NP. Even for classically tractable systems composed of only logarithmically many qubits or free fermions, we show the optimization to be NP-hard. This elucidates that the classical optimization is intrinsically hard and does not merely inherit the hardness from the ground state problem. Our analysis shows that the training landscape can have many far from optimal persistent local minima This means gradient and higher order descent algorithms will generally converge to far from optimal solutions.

Fairness-Based Packing of Industrial IoT Data in Permissioned Blockchains

Abstract: In recent years, blockchain has been broadly applied to industrial Internet of Things (IIoT) due to its features of decentralization, transparency, and immutability. In existing permissioned blockchain based IIoT solutions, transactions submitted by IIoT devices are arbitrarily packed into blocks without considering their waiting times. Hence, there will be a high deviation of the transaction response times, which is known as the lack of fairness. Unfair permissioned blockchain decreases the quality of experience from the perspective of the IIoT devices. Moreover, some transactions can get timeouts if not responded for a long time. In this article, we propose Fair-Pack , the first fairness-based transaction packing algorithm for permissioned blockchain empowered IIoT systems. First, we gain the insight that fairness is positively related to the sum of waiting times of the selected transactions through theoretical analysis. Based on this insight, we transform the fairness problem into the subset sum problem, which is to find a valid subset from a given set with subset sum as large as possible. However, it is time consuming to solve the problem using a brute-force approach because there is an exponential number of subsets for a given set. To this end, we propose a heuristic and a min-heap-based optimal algorithm for different parameter settings. Finally, we analyze the time complexity of Fair-Pack and conduct extensive experiments. The results reveal that Fair-Pack is time-efficient and outperforms the existing algorithms significantly in terms of both fairness and average transaction response time.

Scalable Multi-view Subspace Clustering with Unified Anchors

Abstract: Multi-view subspace clustering has received widespread attention to effectively fuse multi-view information among multimedia applications. Considering that most existing approaches' cubic time complexity makes it challenging to apply to realistic large-scale scenarios, some researchers have addressed this challenge by sampling anchor points to capture distributions in different views. However, the separation of the heuristic sampling and clustering process leads to weak discriminate anchor points. Moreover, the complementary multi-view information has not been well utilized since the graphs are constructed independently by the anchors from the corresponding views. To address these issues, we propose a Scalable Multi-view Subspace Clustering with Unified Anchors (SMVSC). To be specific, we combine anchor learning and graph construction into a unified optimization framework. Therefore, the learned anchors can represent the actual latent data distribution more accurately, leading to a more discriminative clustering structure. Most importantly, the linear time complexity of our proposed algorithm allows the multi-view subspace clustering approach to be applied to large-scale data. Then, we design a four-step alternative optimization algorithm with proven convergence. Compared with state-of-the-art multi-view subspace clustering methods and large-scale oriented methods, the experimental results on several datasets demonstrate that our SMVSC method achieves comparable or better clustering performance much more efficiently. The code of SMVSC is available at https://github.com/Jeaninezpp/SMVSC.

A Hybrid Iterated Greedy Algorithm for a Crane Transportation Flexible Job Shop Problem

Abstract: In this study, we propose an efficient optimization algorithm that is a hybrid of the iterated greedy and simulated annealing algorithms (hereinafter, referred to as IGSA) to solve the flexible job shop scheduling problem with crane transportation processes (CFJSP). Two objectives are simultaneously considered, namely, the minimization of the maximum completion time and the energy consumptions during machine processing and crane transportation. Different from the methods in the literature, crane lift operations have been investigated for the first time to consider the processing time and energy consumptions involved during the crane lift process. The IGSA algorithm is then developed to solve the CFJSPs considered. In the proposed IGSA algorithm, first, each solution is represented by a 2-D vector, where one vector represents the scheduling sequence and the other vector shows the assignment of machines. Subsequently, an improved construction heuristic considering the problem features is proposed, which can decrease the number of replicated insertion positions for the destruction operations. Furthermore, to balance the exploration abilities and time complexity of the proposed algorithm, a problem-specific exploration heuristic is developed. Finally, a set of randomly generated instances based on realistic industrial processes is tested. Through comprehensive computational comparisons and statistical analyses, the highly effective performance of the proposed algorithm is favorably compared against several efficient algorithms.

A Knowledge-Based Cuckoo Search Algorithm to Schedule a Flexible Job Shop With Sequencing Flexibility

Abstract: Scheduling of complex manufacturing systems entails complicated constraints such as the mating operational one. Focusing on the real settings, this article considers an extended version of a flexible job shop problem that allows the precedence between the operations to be given by an arbitrary directed acyclic graph instead of a linear order. In order to obtain its reliable and high-performance schedule in a reasonable time, this article contributes a knowledge-based cuckoo search algorithm (KCSA) to the scheduling field. The proposed knowledge base is initially trained off-line on models before operations based on reinforcement learning and hybrid heuristics to store scheduling information and appropriate parameters. In its off-line training phase, the algorithm SARSA is used, for the first time, to build a self-adaptive parameter control scheme of the CS algorithm. In each iteration, the proposed knowledge base selects suitable parameters to ensure the desired diversification and intensification of population. It is then used to generate new solutions by probability sampling in a designed mutation phase. Moreover, it is updated via feedback information from a search process. Its influence on KCSA’s performance is investigated and the time complexity of the KCSA is analyzed. The KCSA is validated with the benchmark and randomly generated cases. Various simulation experiments and comparisons between it and several popular methods are performed to validate its effectiveness. Note to Practitioners —Complex manufacturing scheduling problems are usually solved via intelligent optimization algorithms. However, most of them are parameter-sensitive, and thus selecting their proper parameters is highly challenging. On the other hand, it is difficult to ensure their robustness since they heavily rely on some random mechanisms. In order to deal with the above obstacles, we design a knowledge-based intelligent optimization algorithm. In the proposed algorithm, a reinforcement learning algorithm is proposed to self-adjust its parameters to tackle the parameter selection issue. Two probability matrices for machine allocation and operation sequencing are built via hybrid heuristics as a guide for searching a new and efficient assignment scheme. To further improve the performance of our algorithm, a feedback control framework is constructed to ensure the desired state of population. As a result, our algorithm can obtain a high-quality schedule in a reasonable time to fulfill a real-time scheduling purpose. In addition, it possesses high robustness via the proposed feedback control technique. Simulation results show that the knowledge-based cuckoo search algorithm (KCSA) outperforms well some existing algorithms. Hence, it can be readily applied to real manufacturing facility scheduling problems.

Complexity growth in integrable and chaotic models

Abstract: We use the SYK family of models with N Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by the appearance and accumulation of conjugate points, which signal the presence of shorter geodesics intersecting the time evolution trajectory. By explicitly locating such “shortcuts” through analytical and numerical methods, we demonstrate that: (a) in the free theory, time evolution encounters conjugate points at a polynomial time; consequently complexity growth truncates at O( $$ \sqrt{N} $$ ), and we find an explicit operator which “fast-forwards” the free N-fermion time evolution with this complexity, (b) in a class of interacting integrable theories, the complexity is upper bounded by O(poly(N)), and (c) in chaotic theories, we argue that conjugate points do not occur until exponential times O(eN), after which it becomes possible to find infinitesimally nearby geodesics which approximate the time evolution operator. Finally, we explore the notion of eigenstate complexity in free, integrable, and chaotic models.

On the (in)security of ROS

Abstract: We present an algorithm solving the ROS (Random inhomogeneities in a Overdetermined Solvable system of linear equations) problem mod p in polynomial time for \(\ell > \log p\) dimensions. Our algorithm can be combined with Wagner’s attack, and leads to a sub-exponential solution for any dimension \(\ell \) with best complexity known so far.

Complexity of Infinite-Domain Constraint Satisfaction

Abstract: Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory

Polarization-Adjusted Convolutional (PAC) Codes: Sequential Decoding vs List Decoding

Abstract: In the Shannon lecture at the 2019 International Symposium on Information Theory (ISIT), Arikan proposed to employ a one-to-one convolutional transform as a pre-coding step before the polar transform. The resulting codes of this concatenation are called polarization-adjusted convolutional (PAC) codes . In this scheme, a pair of polar mapper and demapper as pre- and post- processing devices are deployed around a memoryless channel, which provides polarized information to an outer decoder leading to improved error correction performance of the outer code. In this paper, the list decoding and sequential decoding (including Fano decoding and stack decoding) are first adapted for use to decode PAC codes. Then, to reduce the complexity of sequential decoding of PAC/polar codes, we propose (i) an adaptive heuristic metric, (ii) tree search constraints for backtracking to avoid exploration of unlikely sub-paths, and (iii) tree search strategies consistent with the pattern of error occurrence in polar codes. These contribute to the reduction of the average decoding time complexity from 50% to 80%, trading with 0.05 to 0.3 dB degradation in error correction performance within FER = $10^{-3}$ range, respectively, relative to not applying the corresponding search strategies. Additionally, as an important ingredient in Fano decoding of PAC/polar codes, an efficient computation method for the intermediate LLRs and partial sums is provided. This method is effective in backtracking and avoids storing the intermediate information or restarting the decoding process. Eventually, all three decoding algorithms are compared in terms of performance, complexity, and resource requirements.

Finding Temporal Paths Under Waiting Time Constraints

Abstract: Computing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes over time, gained more and more attention. A path is time-respecting, or temporal, if it uses edges with non-decreasing time stamps. We investigate a basic constraint for temporal paths, where the time spent at each vertex must not exceed a given duration $$\varDelta $$ , referred to as $$\varDelta $$ -restless temporal paths. This constraint arises naturally in the modeling of real-world processes like packet routing in communication networks and infection transmission routes of diseases where recovery confers lasting resistance. While finding temporal paths without waiting time restrictions is known to be doable in polynomial time, we show that the “restless variant” of this problem becomes computationally hard even in very restrictive settings. For example, it is W[1]-hard when parameterized by the distance to disjoint path of the underlying graph, which implies W[1]-hardness for many other parameters like feedback vertex number and pathwidth. A natural question is thus whether the problem becomes tractable in some natural settings. We explore several natural parameterizations, presenting FPT algorithms for three kinds of parameters: (1) output-related parameters (here, the maximum length of the path), (2) classical parameters applied to the underlying graph (e.g., feedback edge number), and (3) a new parameter called timed feedback vertex number, which captures finer-grained temporal features of the input temporal graph, and which may be of interest beyond this work.

Prescribed-time stabilization of a class of nonlinear systems by linear time-varying feedback

Abstract: This note studies the problem of prescribed-time global stabilization of a class of nonlinear systems, where the nonlinear functions are unknown but satisfy a linear growth condition. By using solutions to a class of parametric Lyapunov equations containing a time-varying parameter which goes to infinity as the time approaches to the prescribed convergence time, linear time-varying feedback is designed explicitly to solve the considered problem, with the help of a Lyapunov-like function. It is shown moreover that the control signal is uniformly bounded by a constant depending on the initial condition. Both linear state feedback and linear observer-based output feedback are considered. The effectiveness of the proposed approach is illustrated by a numerical example borrowed from the literature.

Training (Overparametrized) Neural Networks in Near-Linear Time.

Abstract: The slow convergence rate and pathological curvature issues of first-order gradient methods for training deep neural networks, initiated an ongoing effort for developing faster second-order optimization algorithms beyond SGD, without compromising the generalization error. Despite their remarkable convergence rate (independent of the training batch size n), second-order algorithms incur a daunting slowdown in the cost per iteration (inverting the Hessian matrix of the loss function), which renders them impractical. Very recently, this computational overhead was mitigated by the works of [Zhang et al., 2019; Cai et al., 2019], yielding an O(mn²)-time second-order algorithm for training two-layer overparametrized neural networks of polynomial width m. We show how to speed up the algorithm of [Cai et al., 2019], achieving an O(mn)-time backpropagation algorithm for training (mildly overparametrized) ReLU networks, which is near-linear in the dimension (mn) of the full gradient (Jacobian) matrix. The centerpiece of our algorithm is to reformulate the Gauss-Newton iteration as an 𝓁₂-regression problem, and then use a Fast-JL type dimension reduction to precondition the underlying Gram matrix in time independent of M, allowing to find a sufficiently good approximate solution via first-order conjugate gradient. Our result provides a proof-of-concept that advanced machinery from randomized linear algebra - which led to recent breakthroughs in convex optimization (ERM, LPs, Regression) - can be carried over to the realm of deep learning as well.

A Grid-Based Inverted Generational Distance for Multi/Many-Objective Optimization

Abstract: Assessing the performance of Pareto front (PF) approximations is a key issue in the field of evolutionary multi/many-objective optimization. Inverted generational distance (IGD) has been widely accepted as a performance indicator for evaluating the comprehensive quality for a PF approximation. However, IGD usually becomes infeasible when facing a real-world optimization problem as it needs to know the true PF a priori . In addition, the time complexity of IGD grows quadratically with the size of the solution/reference set. To address the aforementioned issues, a grid-based IGD (Grid-IGD) is proposed to estimate both convergence and diversity of PF approximations for multi/many-objective optimization. In Grid-IGD, a set of reference points is generated by estimating PFs of the problem in question, based on the representative nondominated solutions of all the approximations in a grid environment. To reduce the time complexity, Grid-IGD only considers the closest solution within the grid neighborhood in the approximation for every reference point. Grid-IGD also possesses other desirable properties, such as Pareto compliance, immunity to dominated/duplicate solutions, and no need of normalization. In the experimental studies, Grid-IGD is verified on both the artificial and real PF approximations obtained by five many-objective optimizers. Effects of the grid specification on the behavior of Grid-IGD are also discussed in detail theoretically and experimentally.

Improvement of Support Vector Machine Algorithm in Big Data Background

Abstract: With the rapid development of the Internet and the rapid development of big data analysis technology, data mining has played a positive role in promoting industry and academia. Classification is an important problem in data mining. This paper explores the background and theory of support vector machines (SVM) in data mining classification algorithms and analyzes and summarizes the research status of various improved methods of SVM. According to the scale and characteristics of the data, different solution spaces are selected, and the solution of the dual problem is transformed into the classification surface of the original space to improve the algorithm speed. Research Process. Incorporating fuzzy membership into multicore learning, it is found that the time complexity of the original problem is determined by the dimension, and the time complexity of the dual problem is determined by the quantity, and the dimension and quantity constitute the scale of the data, so it can be based on the scale of the data Features Choose different solution spaces. The algorithm speed can be improved by transforming the solution of the dual problem into the classification surface of the original space. Conclusion. By improving the calculation rate of traditional machine learning algorithms, it is concluded that the accuracy of the fitting prediction between the predicted data and the actual value is as high as 98%, which can make the traditional machine learning algorithm meet the requirements of the big data era. It can be widely used in the context of big data.

LQG Control and Sensing Co-Design

Abstract: We investigate a linear-quadratic-Gaussian (LQG) control and sensing codesign problem, where one jointly designs sensing and control policies. We focus on the realistic case where the sensing design is selected among a finite set of available sensors, where each sensor is associated with a different cost (e.g., power consumption). We consider two dual problem instances: sensing-constrained LQG control, where one maximizes a control performance subject to a sensor cost budget, and minimum-sensing LQG control, where one minimizes a sensor cost subject to performance constraints. We prove that no polynomial time algorithm guarantees across all problem instances a constant approximation factor from the optimal. Nonetheless, we present the first polynomial time algorithms with per-instance suboptimality guarantees. To this end, we leverage a separation principle, which partially decouples the design of sensing and control. Then, we frame LQG codesign as the optimization of approximately supermodular set functions; we develop novel algorithms to solve the problems; and we prove original results on the performance of the algorithms and establish connections between their suboptimality and control-theoretic quantities. We conclude the article by discussing two applications, namely, sensing-constrained formation control and resource-constrained robot navigation .

Random Forest Bagging and X-Means Clustered Antipattern Detection from SQL Query Log for Accessing Secure Mobile Data

Abstract: In the current ongoing crisis, people mostly rely on mobile phones for all the activities, but query analysis and mobile data security are major issues. Several research works have been made on efficient detection of antipatterns for minimizing the complexity of query analysis. However, more focus needs to be given to the accuracy aspect. In addition, for grouping similar antipatterns, a clustering process was performed to eradicate the design errors. To address the above-said issues and further enhance the antipattern detection accuracy with minimum time and false positive rate, in this work, Random Forest Bagging X-means SQL Query Clustering (RFBXSQLQC) technique is proposed. Different patterns or queries are initially gathered from the input SQL query log, and bootstrap samples are created. Then, for each pattern, various weak clusters are constructed via X-means clustering and are utilized as the weak learner (clusters). During this process, the input patterns are categorized into different clusters. Using the Bayesian information criterion, the similarity measure is employed to evaluate the similarity between the patterns and cluster weight. Based on the similarity value, patterns are assigned to either relevant or irrelevant groups. The weak learner results are aggregated to form strong clusters, and, with the aid of voting, a majority vote is considered for designing strong clusters with minimum time. Experiments are conducted to evaluate the performance of the RFBXSQLQC technique using the IIT Bombay dataset using the metrics like antipattern detection accuracy, time complexity, false-positive rate, and computational overhead with respect to the differing number of queries. The results revealed that the RFBXSQLQC technique outperforms the existing algorithms by 19% with pattern detection accuracy, 34% minimized time complexity, 64% false-positive rate, and 31% in terms of computational overhead.

Matrix-Based Evolutionary Computation

Abstract: Computational intelligence (CI), including artificial neural network, fuzzy logic, and evolutionary computation (EC), has rapidly developed nowadays. Especially, EC is a kind of algorithm for knowledge creation and problem solving, playing a significant role in CI and artificial intelligence (AI). However, traditional EC algorithms have faced great challenge of heavy computational burden and long running time in large-scale (e.g., with many variables) problems. How to efficiently extend EC algorithms to solve complex problems has become one of the most significant research topics in CI and AI communities. To this aim, this paper proposes a matrix-based EC (MEC) framework to extend traditional EC algorithms for efficiently solving large-scale or super large-scale optimization problems. The proposed framework is an entirely new perspective on EC algorithm, from the solution representation to the evolutionary operators. In this framework, the whole population (containing a set of individuals) is defined as a matrix, where a row stands for an individual and a column stands for a dimension (decision variable). This way, the parallel computing functionalities of matrix can be directly and easily carried out on the high performance computing resources to accelerate the computational speed of evolutionary operators. This paper gives two typical examples of MEC algorithms, named matrix-based genetic algorithm and matrix-based particle swarm optimization. Their matrix-based solution representations are presented and the evolutionary operators based on the matrix are described. Moreover, the time complexity is analyzed and the experiments are conducted to show that these MEC algorithms are efficient in reducing the computational time on large scale of decision variables. The MEC is a promising way to extend EC to complex optimization problems in big data environment, leading to a new research direction in CI and AI.

IPPTS: An Efficient Algorithm for Scientific Workflow Scheduling in Heterogeneous Computing Systems

Abstract: Efficient scheduling algorithms are key for attaining high performance in heterogeneous computing systems. In this article, we propose a new list scheduling algorithm for assigning task graphs to fully connected heterogeneous processors with an aim to minimize the scheduling length. The proposed algorithm, called Improved Predict Priority Task Scheduling (IPPTS) algorithm has two phases: task prioritization phase, which gives priority to tasks, and processor selection phase, which selects a processor for a task. The IPPTS algorithm has a quadratic time complexity as the related algorithms for the same goal, that is $O(t^{2} \times p)$ O ( t 2 × p ) , for $t$ t tasks and $p$ p processors. Our algorithm reduces the scheduling length significantly by looking ahead in both task prioritization phase and processor selection phase. In this way, the algorithm is looking ahead to schedule a task and its heaviest successor task to the optimistic processor, i.e., the processor that minimizes their computation and communication costs. The experiments based on both randomly generated graphs and graphs of real-world applications show that the IPPTS algorithm significantly outperforms previous list scheduling algorithms in terms of makespan, speedup, makespan standard deviation, efficiency, and frequency of best results.

An Ising Hamiltonian solver based on coupled stochastic phase-transition nano-oscillators

Abstract: Combinatorial optimization problems belong to the non-deterministic polynomial time (NP)-hard complexity class, and their computational requirements scale exponentially with problem size. They can be mapped into the problem of finding the ground state of an Ising model, which describes a physical system with converging dynamics. Various platforms, including optical, electronic and quantum approaches, have been explored to accelerate the ground-state search, but improvements in energy efficiencies and computational abilities are still required. Here we report an Ising solver based on a network of electrically coupled phase-transition nano-oscillators (PTNOs) that form a continuous-time dynamical system (CTDS). The bi-stable phases of the injection-locked PTNOs act as artificial Ising spins and the stable points of the CTDS act as the ground-state solution of the problem. We experimentally show that a prototype with eight PTNOs can solve an NP-hard MaxCut problem with high probability of success (96% for 600 annealing cycles). We also show via numerical simulations that our Ising Hamiltonian solver can solve MaxCut problems of 100 nodes with energy efficiency of 1.3 × 107 solutions per second per watt, offering advantages over other approaches including memristor-based Hopfield networks, quantum annealers and photonic Ising solvers. An Ising solver that is based on a network of electrically coupled phase-transition nano-oscillators, which provides a continuous-time dynamical system, can be used to efficiently solve a non-deterministic polynomial time (NP)-hard MaxCut problem.

Incremental Factorization of Big Time Series Data with Blind Factor Approximation

Abstract: Extracting the latent factors of big time series data is an important means to examine the dynamic complex systems under observation. These low-dimensional and “small” representations reveal the key insights to the overall mechanisms, which can otherwise be obscured by the notoriously high dimensionality and scale of big data as well as the enormously complicated interdependencies amongst data elements. However, grand challenges still remain: (1) to incrementally derive the multi-mode factors of the augmenting big data and (2) to achieve this goal under the circumstance of insufficient a priori knowledge. This study develops an incrementally parallel factorization solution (namely I-PARAFAC ) for huge augmenting tensors (multi-way arrays) consisting of three phases over a cutting-edge GPU cluster: in the “giant-step” phase , a variational Bayesian inference ( VBI ) model estimates the distribution of the close neighborhood of each factor in a high confidence level without the need for a priori knowledge of the tensor or problem domain; in the “baby-step” phase , a massively parallel Fast-HALS algorithm (namely G-HALS ) has been developed to derive the accurate subfactors of each subtensor on the basis of the initial factors; in the final fusion phase , I-PARAFAC fuses the known factors of the original tensor and those accurate subfactors of the “increment” to achieve the final full factors. Experimental results indicate that: (1) the VBI model enables a blind factor approximation , where the distribution of the close neighborhood of each final factor can be quickly derived (10 iterations for the test case). As a result, the model of a low time complexity significantly accelerates the derivation of the final accurate factors and lowers the risks of errors; (2) I-PARAFAC significantly outperforms even the latest high performance counterpart when handling augmenting tensors, e.g., the increased overhead is only proportional to the increment while the latter has to repeatedly factorize the whole tensor, and the overhead in fusing subfactors is always minimal; (3) I-PARAFAC can factorize a huge tensor (volume up to 500 TB over 50 nodes) as a whole with the capability several magnitudes higher than conventional methods, and the runtime is in the order of $\frac{1}{n}$ 1 n to the number of compute nodes; (4) I-PARAFAC supports correct factorization-based analysis of a real 4-order EEG dataset captured from a variety of epilepsy patients. Overall, it should also be noted that counterpart methods have to derive the whole tensor from the scratch if the tensor is augmented in any dimension; as a contrast, the I-PARAFAC framework only needs to incrementally compute the full factors of the huge augmented tensor.

An improved simulated annealing algorithm with crossover operator for capacitated vehicle routing problem

Abstract: The capacitated vehicle routing problem (CVRP) is one of the commonly studied issues today. It belongs to the class of NP-hard problems and has a high time complexity. Therefore, the solution of the CVRP was focused in this study. An improved simulated annealing algorithm with crossover operator, called ISA-CO, was proposed. A population based simulated annealing algorithm was used in the proposed algorithm. The solutions in the population were developed through the local search operators, including swap, scramble, insertion, and reversion. The improved 2-opt algorithm was used to develop the routes making up the solution. The partially mapped crossover (PMX) and the order crossover (OX) operators were applied to the solutions in the population to accelerate the convergence. A mix selection method was used to ensure the balance between exploitation and exploration. The ISA-CO was tested on 91 well-known benchmark instances. The results indicated that the method has a better performance compared to other state-of-the-art methods on many instances.