Search

This paper deals with decomposition of complete graphs on $n$ vertices into circulant graphs with reduced degree $r< n-1$ . They are denoted as $C_{n}(a_{1}, a_{2}, {\dots }, a_{m})$ , where $a_{1}$ to $a_{m}$ are generators. Mathematical labeling for such bigger (higher order and huge size) and complex (strictly regular with so many triangles) graphs is very difficult. That is why after decomposition, an edge irregular $k$ -labeling for these subgraphs is computed with the help of algorithmic approach. Results of $k$ are computed by implementing this iterative algorithm in computer. Using the values of $k$ , an upper bound for edge irregularity strength is suggested for $C_{n}(a_{1}, a_{2}, {\dots }, a_{m})$ that is ${\vert E\vert }/{2}\log _{2} \vert V\vert $ .

Online sequential extreme learning machine (OS-ELM) has become a popular online learning strategy for single-hidden layer feedforward neural networks, and complex-valued signals are ubiquitous in real applications. In order to cater for complex-valued signals, especially for noncircular signals, in this paper we extend OS-ELM to complex domain, and propose two augmented online sequential complex ELM models by incorporating the conjugates of the network input and the hidden layer respectively. In this way, the proposed models are equipped with the capability to capture the complete second-order statistics of noncircular signals, which results in the enhanced generalization ability. The corresponding regularized models are derived to avoid the possible overfitting problem. By exploiting the algebra structure resulted from the augmented architecture, several approaches to reducing the computational complexity are also proposed. Simulation results validate the efficiency of the proposed algorithms.

Fuzzy Logic Controller (FLC) as speed controller is preferred in many AC machine drives, due to its ability to handle model non-linearity, speed variations and parameters change. Additionally, Self-Tuning FLC (ST-FLC) is a modified FLC controller to overcome the issues associated with a fixed parameter FLC and to avoid performance degradation of the machine drive. It can update the FLC parameters in accordance to any variation, changes or disturbances that may occur to the drive system. However, FLC system requires huge computation capacity which increases the computational burden of the overall machine drive system and may result in poor performance. This research proposed a simple ST-FLC mechanism to tune the main FLC speed controller. Three different rule-size of FLC (9, 25, and 49) rules are implemented with ST-FLC mechanism based Induction Motor (IM) drive. Performance comparison of the three different rule-size based ST-FLC is conducted based on simulation and experimental analysis. In addition, a computational effort is technically analyzed and compared for the three different rule-size. In the experiment, ST-FLC with less number of rules (9-rules) shows superior performance, lower sampling and lower computational efforts compared to ST-FLC with higher rule-size (25, 49) rules.

Non-orthogonal multiple access (NOMA) has been recognized as an essential technology for beyond fifth-generation (beyond-5G) wireless networks to increase connectivity, spectral efficiency, cell-edge throughput, and user fairness. In this paper, we propose two subcarrier-user assignment algorithms (SUAAs) for the downlink NOMA system to enhance the spectral efficiency, the fairness, the data rate of weak users, and the outage probability. The assignment order of the first proposed SUAA is based on the worst subcarrier first (WSF) to avoid selecting a user with the worst channel gain with any subcarrier and called (WSF-SUAA). On the other hand, the second proposed SUAA is based on spectral efficiency maximization (SEM) and called (SEM-SUAA), but requires exhaustive search. The assignment process of both algorithms is based on making the channel gain of the selected paired users per subcarrier as high as possible to increase the data rate of each user. Besides, the assignment process of strong users for all subcarriers is performed before the assignment process of weak users to increase the total system sum-rate. It is exposed throughout the simulation that the two proposed SUAAs can attain significant improvement in the total spectral efficiency, weak user data rate, outage probability, and user fairness compared to the existing algorithms. While the performances of the two proposed SUAAs are convergent, the computational complexity of WSF-SUAA is significantly lower than that of SEM-SUAA and slightly higher than that of the existing algorithms.

The paper discusses adaptive filtering using Least Mean Square (LMS) and Recursive Least Square (RLS) algorithms. An algorithm for adjusting the coefficients of an adaptive digital filter in the Residue Number System and a procedure of developed algorithm applying depending on filter length and signal length are proposed. Mathematical modeling of the considered algorithms is performed. Examples are presented to demonstrate how the proposed technique can help the designer in the adjustment of the filter coefficients without the need for extensive trial-and-error procedures. The analysis of the denoising quality and computational complexity is made. Synthetic and real data (earthquake recording) were used while testing. The proposed algorithm surpasses the existing ones like LMS and RLS, and their modifications in a number of parameters: adaptation (denoising) quality, ease of implementation, execution time. The main difference between the developed algorithm is the sequential adaptation of each coefficient with zero error. In the known algorithms, the entire vector of coefficients is iteratively adapted, with some specified accuracy. The iterations (steps) number is determined by the input signal length for all algorithms.

The problem of computing the Sparse Fast Fourier Transform(sFFT) of a $K$ -sparse signal of size $N$ has received significant attention for a long time. The first stage of sFFT is hashing the frequency coefficients into $B(\approx {K})$ buckets named frequency bucketization. The process of frequency bucketization is achieved through the use of filters: Dirichlet kernel filter, aliasing filter, flat filter, etc. The frequency bucketization through these filters can decrease runtime and sampling complexity in low dimensions. It is a hot topic about sFFT algorithms using the flat filter because of its convenience and efficiency since its emergence and wide application. The next stage of sFFT is the spectrum reconstruction by identifying frequencies that are isolated in their buckets. Up to now, there are more than thirty different sFFT algorithms using the sFFT idea as mentioned above by their unique methods. An important question now is how to analyze and evaluate the performance of these sFFT algorithms in theory and practice. In this paper, it is mainly discussed about sFFT algorithms using the flat filter. In the first part, the paper introduces the techniques in detail, including two types of frameworks, five different methods to reconstruct spectrum and corresponding algorithms. We get the conclusion of the performance of these five algorithms, including runtime complexity, sampling complexity and robustness in theory. In the second part, we make three categories of experiments for computing the signals of different SNR, different $N$ , and different $K$ by a standard testing platform and record the run time, percentage of the signal sampled, and $L_{0},L_{1},L_{2}$ error both in the exactly sparse case and general sparse case. The result of experiments is consistent with the inferences obtained in theory. It can help us to optimize these algorithms and use them correctly in the right areas.

Radio resource management (RRM) for future fifth-generation (5G) heterogeneous networks (HetNets) has emerged as a critical area due to the increased density of small-cell networks and radio access technologies. Recent research has mostly concentrated on resource management, including spectrum utilization and interference mitigation, but the complexities of these resources have been given little attention. This paper provides an overview of the issues arising from future 5G systems and highlights their importance. The different approaches used in recently published surveys categorizing RRM schemes are discussed, and the survey method is presented. We report on a survey of HetNet RRM schemes that have been studied recently, with a focus on the joint optimization of radio resource allocation with other mechanisms. These RRM schemes were subcategorized according to their optimization metrics and qualitatively analyzed and compared. An analysis of the complexity of RRM schemes in terms of implementation and computation is presented. Several potential scopes of research for future RRM in 5G HetNets are also identified.

In view to the unstable navigation risk assessment and make the future navigation risk forecasting, an innovative decision and forecasting approach is put forward in this study. Different from the existing literature, at the current time step, we first deduce an enhanced evidence combination rule to integrate uncertain and conflicting evidences by using weighted basic probabilistic assignment and matrix operation. As a result, a stable decision is effectively achieved no matter what characteristics of the available evidences are. Further, an improved α-β filter is designed with its adaptive coefficients in the novel filtering framework in order to forecast the future navigation risk. What's more, it is an excellent communication between the combined basic probabilistic assignment and the improved α-β filter for the first time. After the deep analysis of the computational complexity, a plenty of numeric simulations and actual experiments are provided to indicate the reliability and efficiency of the proposed approach.

The alternating direction method of multipliers (ADMM) is one of most foundational algorithms for linear constrained composite minimization problems. For different specific problems, variations of ADMM (like linearized ADMM, proximal ADMM) are developed. By using the Bregman distances, lots of ADMMs can be formulated into a uniform mathematical scheme. Although variational inequalities have been well used to study ADMMs, the use for BADMM has still been missing. In this paper, we study the convergence of BADMM by variational inequalities. We present a proof framework for BADMMs. And then, we present very concise convergence proof for the basic BADMM. As applications, we consider several variations of BADMM and obtain corresponding convergence results.

Fulcrum coding combines a high-field outer Random Linear Network Coding (RLNC) that generates outer coding expansion packets with a small-field inner RLNC that combines the source packets and the outer coding expansion packets. This two-layer Fulcrum coding allows flexible decoding in receivers with heterogeneous computational capabilities. Fulcrum coding has so far only been studied for conventional dense RLNC, which randomly selects all coding coefficients, and only for a statically fixed number of outer expansion packets. However, the probability that the coding coefficient row of a newly received packet is linearly independent of prior received coding coefficient rows (a prerequisite for successful decoding) is highly dynamic. We propose to exploit the dynamics of this probability to reduce the computational complexity of Fulcrum coding. In particular, we vary the density of non-zero coding coefficients, i.e., equivalently, the sparsity of coding coefficients, and the number of outer expansion packets to keep the complexity low while maintaining a reasonably high decoding probability. We introduce the general principles of dynamic sparsity and expansion packets (DSEP) for Fulcrum coding as well as two specific example DSEP policies. Our evaluations indicate that DSEP Fulcrum can increase the encoding throughput tenfold and increase the decoding throughput 1.4 to 4.3 fold while achieving decoding probabilities that are typically less than 1% lower than the conventional Fulcrum decoding probabilities. We also find that DSEP achieves somewhat higher encoding and decoding throughputs than the CodornicesRq (Release 2.1) implementation of RaptorQ block coding for small blocks (generations) of source packets, while RaptorQ is substantially faster for large generation sizes. Furthermore, we develop and evaluate an elementary DSEP recoding mechanism that achieves a recoding throughput more than double the decoding throughput.

Universal Filtered Multi-Carrier (UFMC) is a promising multi-carrier modulation scheme. It can be considered as the combine of filtered OFDM and Filter Bank Multi-Carrier (FBMC) modulations. The difference among them is that filtered OFDM filters the entire band and FBMC filters the single subcarrier, while UFMC filters groups of subcarriers. It is evaluated their performance for the new conditions. While UFMC offers superior advantages, such as higher spectral efficiency, lower overhead, more robustness and less out-of-band (OOB) emission, the introduction of filters and the application of FFTs for the subband increase the implementation complexity of the transmitter. In terms of complexity, based on the analysis of UFMC transceiver structure, few low complexity implementation methods for UFMC systems are recently put forward. The low complexity solutions need to be found. In this paper, the computational complexity of different UFMC implementation methods based on lightweight structure which combines with the FIR filter and the poly-phase filter is evaluated. It is shown that the computational complexity of the UFMC transmitter can be reduced to be similar to OFDM, which is a promising solution for the advanced waveform. In addition, we analyze the effect of the filter on the power spectral density (PSD) of the proposed structure. Analysis shows that the system can be implemented with better performance by adjusting the filter parameters.

Cognitive radio sensor network (CRSN) is an intelligent and reasonable combination of cognitive radio and wireless sensor networks. Clustering is an effective method to manage the network topology of CRSN. In order to solve the optimal cluster head selection problem in clustering which is proved to be NP-hard, inspired by ions motion optimization (IMO) algorithm, a novel centralized clustering routing protocol, i.e., IMO-based clustering routing protocol (IMOCRP) which can adapt to the dynamic characteristics of CRSN is presented in this paper. Optimal number of clusters and identity of cluster heads are automatically determined by combining the excellent characteristics of IMO algorithm and the rich resource, comprehensive information at the sink together. Thanks to its centralized structure, IMOCRP proposed in this paper avoids excessive overhead in cluster head selection and cluster formation, which in turn helps conserve energy. Available channel list at each living node is taken into consideration to perform reasonable channel allocation for clusters, and the probability of collisions with primary users can be reduced, which promotes more successful information delivery. Simulation results have shown that IMOCRP can balance network lifetime and effective information collection capability, and it is superior to other competing protocols.

In this paper, we propose an efficient algorithm for reducing the computational complexity of dynamic time warping (DTW) for obtaining similarity measures between time series. The DTW technique exhibits superior classification accuracy compared to other algorithms but has a limitation of high computational complexity. To reduce the computational complexity of standard DTW, constrained DTW and fast DTW techniques have been proposed. The constrained DTW technique reduces the computational complexity of standard DTW by only considering limited alignments and prevent excessive alignments between two time series, which can reduce the overall classification accuracy. However, since the searching window for limited alignments is fixed, the computational complexity is still high when the length of time series is long. In contrast, fast DTW has a lower classification accuracy than the constrained DTW technique. However, fast DTW estimates the optimal alignment while considering only the alignments within an adaptive window; as two time series increase in length, the fast DTW technique more strongly reduces the computational complexity. Therefore, we propose a fast constrained DTW approach that applies the optimal alignment estimation of fast DTW within the limited alignments of constrained DTW. As the proposed fast constrained DTW operates within a fixed window area of the constrained DTW, which prevents excessive alignments, it has a classification accuracy similar to that of the constrained DTW. Also, in the fast constrained DTW, when the length of the time series is long, a low computational complexity is maintained by the influence of the adaptive window of the fast DTW. Experimental results on 19 UCR time series datasets show that the proposed fast constrained DTW method achieves computational complexity reductions of approximately 52.2% and 22.3% compared to the existing fast DTW and constrained DTW, while maintaining almost the same classification accuracy as the constrained DTW.

Regularized zero forcing (RZF) precoding is an efficient linear precoding scheme for combating interference in a single-cell massive multiple-input-multiple-output (MIMO) systems. Inaccurate channel state information (CSI) due to channel aging will reduce the performance of the precoder over time. The channel aging determines how often we need to estimate the channels, and thus how frequently we need to send pilots in order to maximize the overall data rate. Channel prediction is one way to improve the CSI accuracy in the downlink, without having to send new pilots but it requires frequent re-computation of the matrix inverse in the RZF precoder, which has high-computational complexity. In this paper, we consider massive MIMO-OFDM systems and propose an algorithm called inverse extrapolation that extrapolates the channel and inverse matrix coefficients separately. The RZF coefficients are then obtained with comparably low complexity with no need for matrix inversion. We compare this algorithm with the traditional way of computing the RZF coefficients through prediction of the channel matrix followed by matrix inversion. The simulation results show that the two predictors have the same performance when the number of antennas is large, and thus the proposed scheme is preferable since it can reduce the complexity. For example, a scenario is shown, where the complexity is reduced by 61.84% without a significant degradation in performance. Funding Agencies|Beijing Natural Science Foundation [L182038]; National Natural Science Foundation for Distinguished Young Scholars of China [61325006]; Swedish Research Council (VR); ELLIIT

The application of orthogonal frequency division multiplexing (OFDM) has become more and more widespread in recent years. However, the high peak-to-average power ratio (PAPR) problem is still one of the critical issues in the implementation of OFDM systems. Among the techniques of PAPR reduction, iterative clipping and filtering (ICF) is widely used due to its easy implement, and many ICF-based methods have been proposed recently. The optimized ICF (OICF) further has been designed with an optimized filter and achieves faster convergence rate. And the simplified OICF (SOICF) applies Lagrange multiplier method to simplify the problem solving as compared to OICF. The approach saves SOICF from using complicated convex optimization methods. Most recently the clipping-noise compression (CNC) method is proposed to reduce the required number of Fourier transforms by compressing the clipping noise in the time domain. Based on SOICF, this paper adopts clipping and noise compression to replace the calculation of PAPR-reduction vector in each iteration. Analysis shows that the computational complexity of the proposed scheme is lower than SOICF. In addition, we have improved the CNC technique and introduced a compression threshold in the proposed scheme. In each iteration, only the components whose amplitude exceeds the compression threshold are compressed, while the others remain unchanged. To this end, this reduces the amount of information lost, resulting in better BER performance. The simulation results show that the proposed scheme has better BER performance than SOICF, and better PAPR reduction than CNC. When equal amounts of PAPR reduction by the evaluated methods are actually achieved, the BER performance of the proposed scheme is better than SOICF and CNC, especially with high-order modulation or lower clipping ratio.

The planning and scheduling of container terminal logistics systems (CTLS) are the multi-objective and multiple strong constraints combinatorial optimization challenges under the uncertain environments, and those are provided with high goal orientation, dynamics, context-sensitivity, coupling, timeliness, and complexity. The increasingly sophisticated decision-making for CTLS is one of the most pressing problems for the programming and optimization method available. This paper discusses CTLS in terms of logistics generalized computation complexity based on computational thinking, great principles of computing, and computational lens, which three are abbreviated with 3CTGPL, and makes a definition of container terminal oriented logistics generalized computational complexity (CTO-LGCC) and container terminal logistics generalized computation comprehensive performance perspective (CTL-GCCPP) from the dimensions of time, space, communication, processor, and memory access. Both can analyze, generalize, migrate, translate, localize, modificate, and evaluate the above-complicated problems and lay solid foundations and establish a feedback improvement framework for the computational model and scheduling algorithms of the CTLS, which is an essential complement to the modeling and optimization methodology and solutions to CTLS with computational logistics. Finally, aimed at the logistics service cases for a large-scale container terminal, the simulation is designed and implemented for different scheduling algorithms, and the qualitative and quantitative comprehensive analysis is executed for the concomitant CTO-LGCC that demonstrates and verifies the feasibility and credibility of the CTO-LGCC and CTL-GCCPP from the viewpoint of the practice of container terminal decision-making support on the tactical level.

We propose SmartGrid, a new video-retargeting method that preserves a shape of the salient object and maintains a temporal coherence for the static background regions in the video. Previous methods mainly focus on preserving the shape of the salient object or maintaining the temporal coherence for each region. However, these methods do not explicitly adjust the sizes of the grids corresponding to the salient objects and the static background regions. Thus, they have difficulty in maintaining the consistency of the salient object shape and the temporal coherence for the static background regions. The basic idea of SmartGrid is to maintain the consistency of the contents in consecutive frames by analyzing the degree of the spatiotemporal consistency. Compared to the best results obtained using eight previous methods, SmartGrid achieved improvements of 1.19× in Bidirectional Similarity Measure, 7.59× in Jittery Metric 1, and 13.16× in Jittery Metric 2, and reduced the average computation time per pixel by 6.14×.

Radar detection of high-speed targets suffers from range walks during the integration time. Methods in current use for mitigating range walks are beset by high computational complexity therein that hinders practical real-time processing. In this context, we exploit the sparsity of the target echo in the transform domain and propose an efficient range walk mitigation algorithm based on sparse Fourier transform (SFT). Concretely, the input long echo sequence is first divided into short overlapped segments with an SFT bucket structure. Then, speed compensation is performed to the short segments, which involves less complex multiplications. Subsequently, SFT is employed which efficiently obtains the Fourier transform of the long sequence such that the range alignment of the multi-pulse echo is accomplished. As such, the proposed SFT-based algorithm significantly reduces the amount of complex multiplications required in speed compensation and long sequence transform, and thus substantially improves the computational efficiency. In this paper, the selection of the window function and the length of segments are examined for their influence on the detection performance with different signal-to-noise ratios. The superiorities of the proposed algorithm in both detection performance and computational efficiency are demonstrated by numerical experiments. The proposed algorithm can potentially find applications in other radar systems such as synthetic aperture radars, inverse synthetic aperture radars, and so on where echo range walk is also encountered.

In remote cardiac care monitoring applications, electrocardiogram (ECG) signals are contaminated by artifacts during data acquisition and transmission of signals. The removal of the artifacts is an important task for proper diagnosis. In this paper, an attempt has been made to remove the artifacts, especially baseline wander (BW), muscle artifacts (MA), power line interference (PLI), and electrode motion (EM) using a least mean logarithmic squares (LMLS) algorithm. Further to improve the filtering ability and speed up the convergence process, data normalization is applied. The above algorithm can be normalized with reference to maximum data normalization which leads to reduced computational complexity in the denominator. Based on the above algorithms, various adaptive signal enhancers (ASE's) are developed. To reduce the computational complexity of the signal enhancer, the proposed ASE's are combined with sign-based algorithms. The proposed ASE's are tested on real ECG signals obtained from the MIT-BIH database to compare the performance. The simulation results obtained illustrate that the block-based algorithms are better than LMLS in terms of the signal to noise ratio (SNR), excess mean square error, and computational complexity. Among the LMLS variants, the BB-SRNLMLS-based ASE's have better filtering ability with a reduced number of computations. The improvement of the SNR achieved in the process through the use of BB-SRNLMLS-based ASE's are calculated as 13.2945 dBs, 12.4589 dBs, 16.4289 dBs, and 13.6423 dBs, respectively, for BW, MA, PLI, and EM artifacts.

This work presents an in-depth analysis of the majority of the deep neural networks (DNNs) proposed in the state of the art for image recognition. For each DNN multiple performance indices are observed, such as recognition accuracy, model complexity, computational complexity, memory usage, and inference time. The behavior of such performance indices and some combinations of them are analyzed and discussed. To measure the indices we experiment the use of DNNs on two different computer architectures, a workstation equipped with a NVIDIA Titan X Pascal and an embedded system based on a NVIDIA Jetson TX1 board. This experimentation allows a direct comparison between DNNs running on machines with very different computational capacity. This study is useful for researchers to have a complete view of what solutions have been explored so far and in which research directions are worth exploring in the future; and for practitioners to select the DNN architecture(s) that better fit the resource constraints of practical deployments and applications. To complete this work, all the DNNs, as well as the software used for the analysis, are available online., Will appear in IEEE Access

We introduce the problem of optimizing the constrained estimate of random walks on the probability networks (which are formally defined as the weighted directed graphs in which the total outgoing weight of any node is at most 1). In this problem, it is required to find the size-constrained set of nodes, which maximized the hitting probability (before the time limit) of the randomly initialized random walk. The problem is proved NP-Hard, and we propose an algorithm with polynomial time complexity and constant approximation ratio.

Cross-label suppression dictionary learning is an effective approach to preserve the label property for signal representation in face recognition. This paper presents a proposed improved dictionary learning algorithm, considering the tradeoffs between the operating time and the signal reconstruction residuals for the face recognition problem that combines an optimal loss function and the cross-label suppression supervised dictionary learning approach. Based on the relationship of the cost time of the dictionary learning algorithm and the residuals of the sparse representations, this paper attempts to select an optimal sparse coding dimension for the original signal to reduce the computational cost. Experiments on face recognition confirm that our proposed algorithm is able to achieve a desired classification results as well as obtain a considerably faster dictionary learning process.

The problem of influence maximization (IM) has been extensively studied in recent years and has many practical applications such as social advertising and viral marketing. Given the network and diffusion model, IM aims to find an influential set of seed nodes so that targeting them as diffusion sources will trigger the maximum cascade of influenced individuals. The largest challenge of the IM problem is its NP-hardness, and most of the existing approaches are with polynomial time complexity, making themselves unscalable to very large networks. To address this issue, in this paper, we propose LAIM: a linear time iterative approach for efficient IM on large-scale networks. Our framework has two steps: 1) influence approximation and 2) seed set selection. In the first step, we propose an iterative algorithm to compute the local influence of a node based on a recursive formula and use the local influence to approximate its global influence. In the second step, the $k$ influential seed nodes are mined based on the approximated influence in the first step. Based on our model, we theoretically prove that the proposed approach has linear time and space complexity. We further accelerate our algorithm with simple modifications and propose its fast version. Experimental results on eight real-world large-scale networks exhibit the superiority of our approach over the state-of-the-art methods in terms of both effectiveness and efficiency.

With the proliferation of millimeter-Wave (mm-Wave) systems and visible light communications (VLCs), indoor localization may find multiple applications. When high localization accuracy is required and triangulation is not possible due to the infrastracture and scenario limitations, the computational complexity of searching on a virtual grid may become excessive. In this paper, we amalgamate uplink mm-Wave-based and downlink VLC-based localization. We employ quantum search algorithms for reducing the computational complexity required for achieving the optimal full-search-based performance. Regarding the uplink mm-Wave-based localization, we employ a single anchor equipped with multiple antenna elements and we exploit the specular multipath components created by the room's walls. The proposed solutions outperform the state-of-the-art algorithms. Furthermore, various channel models are considered based on real indoors mm-Wave measurements. By using the VLC-based triangulation for downlink and the proposed mm-Wave-based localization algorithm for uplink, there was an average positioning error of 5.6 cm in the room considered, while requiring 261 database queries on average.

Memory-based recommender systems with $m$ users and $n$ items typically require $O(mn)$ space to store the rating information. In item-based collaborative filtering (CF) algorithms, the feature vector of each item has length $m$ , and it takes $O(m)$ time to compute the similarity between two items using the Pearson or cosine distances. In this paper, we propose an efficient CF algorithm based on a new measure called the $M$ -distance, which is defined as the difference between the average ratings of two items. In the initialization stage, we compute the average ratings of items and store them in two vectors, which requires $O(m)$ space. Scanning the rating dataset then takes $O(mn)$ time. In the online prediction stage, a threshold $\delta $ is employed to identify similar items. To predict $p$ ratings, our algorithm requires $O(np)$ time compared with the $O(mnp)$ time of the cosine-based $k$ NN algorithm. Experiments are undertaken on four well-known datasets, and the proposed $M$ -distance is compared with the cosine-based $k$ NN, Pearson-based $k$ NN, and Slope One methods. Our results show that the new algorithm is significantly faster than the conventional techniques, especially for large datasets, and that its prediction ability is no worse in terms of the mean absolute error and root mean square error.

In large-dimensional wireless systems, such as Cooperative Multi-cell Processing (CoMP), mm-Wave and massive MIMO systems, or cells having a high user density, such as airports, train stations and metropolitan areas, sufficiently accurate estimation of all the channel gains is required for performing coherent detection. Therefore they may impose an excessive complexity. As an attractive design alternative, differential modulation relying on non-coherent detection may be invoked for eliminating the requirement for channel estimation at the Base Station, although at the cost of some performance degradation. In this treatise we propose low-complexity Hard-Input Hard-Output (HIHO), Hard-Input Soft-Output (HISO), as well as Soft-Input Soft-Output (SISO) Quantum-assisted Multiple Symbol Differential Detectors (QMSDD) which perform equivalently to the optimal, but highly complex Maximum A posteriori Probability (MAP) MSDDs in multi-user systems, where the users are separated both in the frequency domain and in the time domain. When using an MSDD, the detection of a user’s symbols is performed over windows of differentially modulated symbols, hence they exhibit an increased complexity with respect to the Conventional Differential Detector (CDD), while simultaneously improving the performance of the system, especially at high Doppler frequencies

Ultra-dense network (UDN) is considered as a promising technology in 5G wireless networks. In an UDN network, dynamic traffic patterns can lead to a high computational complexity and an excessive communications overhead with traditional resource allocation schemes. In this paper, a new resource allocation scheme presenting a low computational overhead and a low subband handoff rate in a dynamic ultra-dense heterogeneous network is presented. The scheme first defines a new interference estimation method that constructs network interference state map, based on which a radio resource allocation scheme is proposed. The resource allocation problem is a MAX-K cut problem and can be solved through a graph- theoretical approach. System level simulations reveal that the proposed scheme decreases the subband handoff rate by 30% with less than 3.2% network throughput degradation.