Conventional Greedy Algorithm Research Articles

Learning automata-accelerated greedy algorithms for stochastic submodular maximization

Submodular function maximization is a typical combinatorial optimization problem that arises in many areas of computer science, such as data summarization, batch mode active learning, and recommendations. We focus on the stochastic submodular maximization (SSM) problems, where an unknown monotonic submodular function is to be maximized under cardinality constraints. Previous research commonly relied on the Monte-Carlo method to assess the stochasticity in submodular functions, which is challenged by the accuracy–efficiency dilemma. Achieving high accuracy requires a large number of Monte-Carlo simulations, while efficiency necessitates the minimization of simulation costs. In this paper, we propose a new family of greedy algorithms based on learning automata (LA) for SSM problems. By exploring the solution space more efficiently, the proposed LA-based greedy family accelerates conventional greedy algorithms. Instead of massively evaluating the expected benefits of each element indiscriminately, an LA-based learning strategy is designed to quickly identify the optimal element among all candidates. Based on the strategy, we present a primitive greedy algorithm and two improved variants, along with proofs of the same approximation guarantee as conventional greedy algorithms. We conducted experiments on three representative SSM tasks, nonparametric learning for structured data, exemplar-based clustering for unstructured data, and influence maximization for graph data. The results verified the advantage of the proposed LA-based greedy family against previous greedy algorithms.

Experimental Demonstration of a Novel Multi-User Bit and Power Loading Algorithm for OFDM-NOMA PON

In this paper, we conduct an extensive investigation on our recently proposed greedy orthogonal frequency division multiplexing non-orthogonal multiple access (OFDM-NOMA) bit and power allocation (GONBP) algorithm, and further propose a novel margin-based OFDM-NOMA bit and power allocation (MONBP) algorithm for multi-user direct-detection (DD) OFDM-NOMA passive optical network (PON). Both algorithms allocate bits and power at both the user level and the subcarrier level by considering the frequency-selective fading effect of all users, the interaction/interference between users, and the constraint of total allocated bits for each user. 43-76Gbit/s PON experiments where two optical network units have different transmission distances of 10-20 km and/or different received optical powers are performed. The results show that the proposed GONBP and MONBP outperform conventional OFDM-NOMA, discrete-Fourier-transform spread OFDM-NOMA, conventional greedy algorithm, and Chow's algorithm. Compared to GONBP, the proposed MONBP greatly reduces the complexity and achieves better performance especially when the signal-to-noise ratio profiles of ONUs are different, thus providing a promising solution for multi-user OFDM-NOMA PON.

Performance Analysis of Resource Allocation Algorithm Based on Simple Particle Swarm Optimization for Device to Device Communication System

The development of Device-to-Device (D2D) communication as an alternative communication scheme continues to grow. D2D communication enables each device to communicate directly with other devices without going through the Evolved Node B (eNB). These days, D2D communication can be implemented in conventional cellular communication, and use the same spectrum as the conventional cellular user (underlay). This underlay scheme can improve the cell’s spectrum efficiency, but the interference level that happens in the cell is increased. Because D2D communication and cellular communication use the same spectrum, there will be interference between D2D user equipment (DUE) and Cellular user Equipment (CUE). A well-designed radio resource allocation is needed to reduce the interference level, while maintaining the overall performance of the cell. In this research, Simplified Particle Swarm Optimization (SPSO) is proposed to overcome this problem. SPSO is a PSO-based algorithm with a limited number of iterations designed to halt calculations when the PSO algorithm cannot find a solution. If SPSO exceeds the limit iteration, a greedy algorithm is executed to do the allocation process. From the simulation, the SPSO algorithm can achieve 1.3310 × 108 bps, 12.3239 bps/Hz, 2.1328 × 103 bps/Watt and 92% on total sumrate, spectral efficiency, power efficiency, and system fairness respectively. These number is better if compared with the conventional greedy allocation algorithm. The total sumrate, spectral efficiency, and power efficiency are increased by 0.9%, 0.74%, and 0.95% in average datarate, spectral efficiency, and power efficiency respectively. Meanwhile the SPSO’s system fairness is decreased by 1.65% compared with the conventional greedy algorithm.

Fairness Guaranteed and Auction-Based x-Haul and Cloud Resource Allocation in Multi-Tenant O-RANs

The open-radio access network (O-RAN) embraces cloudification and network function virtualization for base-band function processing by dis-aggregated radio units (RUs), distributed units (DUs), and centralized units (CUs). These enable the cloud-RAN vision in full, where multiple mobile network operators (MNOs) can install their proprietary or open RUs, but lease on-demand computational resources for DU-CU functions from commonly available open-clouds via open x-haul interfaces. In this paper, we propose and compare the performances of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min-max fairness</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Vickrey-Clarke-Groves (VCG) auction</i> -based x-haul and DU-CU resource allocation mechanisms to create a multi-tenant O-RAN ecosystem that is sustainable for small, medium, and large MNOs. The min-max fair approach <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">minimizes the maximum OPEX of RUs</i> through cost-sharing proportional to their demands, whereas the VCG auction-based approach <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">minimizes the total OPEX for all resources utilized while extracting truthful demands from RUs</i> . We consider time-wavelength division multiplexed (TWDM) passive optical network (PON)-based x-haul interfaces where PON virtualization technique is used to flexibly provide optical connections among RUs and edge-clouds at macro-cell RU locations as well as open-clouds at the central office locations. Moreover, we design efficient heuristics that yield significantly better economic efficiency and network resource utilization than conventional greedy resource allocation algorithms and reinforcement learning-based algorithms.

UAV Trajectory Design and Power Optimization for Terahertz Band-Integrated Sensing and Communications

Sixth generation (6G) wireless networks require very low latency and an ultra-high data rate, which have become the main challenges for future wireless communications. To effectively balance the requirements of 6G and the extreme shortage of capacity within the existing wireless networks, sensing-assisted communications in the terahertz (THz) band with unmanned aerial vehicles (UAVs) is proposed. In this scenario, the THz-UAV acts as an aerial base station to provide information on users and sensing signals and detect the THz channel to assist UAV communication. However, communication and sensing signals that use the same resources can cause interference with each other. Therefore, we research a cooperative method of co-existence between sensing and communication signals in the same frequency and time allocation to reduce the interference. We then formulate an optimization problem to minimize the total delay by jointly optimizing the UAV trajectory, frequency association, and transmission power of each user. The resulting problem is a non-convex and mixed integer optimization problem, which is challenging to solve. By resorting to the Lagrange multiplier and proximal policy optimization (PPO) method, we propose an overall alternating optimization algorithm to solve this problem in an iterative way. Specifically, given the UAV location and frequency, the sub-problem of the sensing and communication transmission powers is transformed into a convex problem, which is solved by the Lagrange multiplier method. Second, in each iteration, for given sensing and communication transmission powers, we relax the discrete variable to a continuous variable and use the PPO algorithm to tackle the sub-problem of joint optimization of the UAV location and frequency. The results show that the proposed algorithm reduces the delay and improves the transmission rate when compared with the conventional greedy algorithm.

Energy Efficient D2D Communication Under Downlink Heterogeneous Network

The increase in cellular users (CU) caused data traffic congestion on the Base Station (BS). Device to Device (D2D) communication can be used to reduce the traffic on BS. D2D communication is direct communication between devices without using a central BS to reduce traffic congestion. CU and D2D users will share the same Resource Block (RB), but there is a drawback that causes interference. This study employs a downlink direction Heterogeneous Network (HetNet) system model to mitigate interference issues. Resource allocation is performed using a greedy algorithm, and to enhance its performance, two small cell base stations (SB) were incorporated, denoted as SB1 (1st SB) and SB2 (2nd SB), thereby transforming the algorithm into a greedy algorithm with SB1SB2. A comparative analysis was conducted between the greedy algorithm with SB1SB2 and the conventional greedy algorithm (without the addition of SB1 and SB2). Furthermore, the authors manipulated the radius of the macro cell base station (MB) in this study to examine its impact on system performance. The results obtained from the simulation are greedy with the SB1SB2 algorithm getting a lower value on the sum data rate with a value of 1.62 × 108 bps, spectral efficiency with a value of 9.02 bps/Hz, total fairness (CU and D2D) with a value of 0.4095. Meanwhile, in terms of power efficiency, the greedy algorithm with SB1SB2 has a higher value of 10.40%. However, resource allocation in both algorithms is not the best solution. So that the resulting performance parameters are less than optimal.&#x0D;

Hybrid Discrete Particle Swarm Optimization Algorithm with Genetic Operators for Target Coverage Problem in Directional Wireless Sensor Networks

For a sensing network comprising multiple directional sensors, maximizing the number of covered targets but minimizing sensor energy use is a challenging problem. Directional sensors that can rotate to modify their sensing directions can be used to increase coverage and decrease the number of activated sensors. Solving this target coverage problem requires creating an optimized schedule where (1) the number of covered targets is maximized and (2) the number of activated directional sensors is minimized. Herein, we used a discrete particle swarm optimization algorithm (DPSO) combined with genetic operators of the genetic algorithm (GA) to compute feasible and quasioptimal schedules for directional sensors and to determine the sensing orientations among the directional sensors. We simulated the hybrid DPSO with GA operators and compared its performance to a conventional greedy algorithm and two evolutionary algorithms, GA and DPSO. Our findings show that the hybrid scheme outperforms the greedy, GA, and DPSO algorithms up to 45%, 5%, and 9%, respectively, in terms of maximization of covered targets and minimization of active sensors under different perspectives. Finally, the simulation results revealed that the hybrid DPSO with GA produced schedules and orientations consistently superior to those produced when only DPSO was used, those produced when only GA was used, and those produced when the conventional greedy algorithm was used.

Uncertainty and multi-criteria global sensitivity analysis of structural systems using acceleration algorithm and sparse polynomial chaos expansion

Sparse polynomial chaos expansion (PCE) can be used to emulate the stochastic model output where the original model is computationally expensive. It is a powerful tool in efficient uncertainty quantification and sensitivity analysis. Structural systems are usually associated with high dimensional and probabilistic input. The number of candidate basis functions increases significantly with input dimension, resulting in high computational burden for establishing sparse PCE. In this study, acceleration techniques are integrated to formulate an algorithm for efficient computation of sparse PCE (ASPCE). The integrated algorithm can improve efficiency of computational process compared with conventional greedy algorithm while ensuring the satisfying predictive performance. Once the sparse PCE model is obtained, the statistic moments, probability density function of stochastic output, and global sensitivity index could be computed efficiently. Traditional PCE based global sensitivity analysis only assesses the sensitivity on individual structural performance criterion. Assessing the global sensitivity considering multiple criteria is challenging as the sensitive parameters may not be consistent for different performance criteria. To address this issue, a two-stage multi-criteria global sensitivity analysis algorithm is proposed by coupling ASPCE and the technique for order preference by similarity to ideal solution (TOPSIS). A holistic global sensitivity index is proposed to identify the sensitive parameters incorporating multiple performance criteria. In order to illustrate the efficiency, accuracy, and applicability of the proposed approach, two illustrative cases are presented.

Caching-Aware Garbage Collection to Improve Performance and Lifetime for NAND Flash SSDs

More and more consumer electronics, such as personal computers and smart phones, adopt NAND flash memory as their data storage devices. However, garbage collection (GC) operations in flash memory may degrade both the performance and lifetime for consumer electronics due to the extra page reads and page writes caused by GC. Greedy algorithm, which selects the block with the least valid pages for GC, is usually used for victim block selection so as to reduce page movements. In this paper, to further improve GC performance, we propose a novel caching-aware GC scheme, and its basic idea is to take into account the pages cached in memory so as to further reduce page movements during GC. We also develop a consistent caching scheme to ensure data consistency and revise the victim block selection process with a lightweight caching-aware block selection scheme. We validate the performance of our caching-aware GC on FlashSim, and results show that it improves the performance of SSDs and prolongs their lifetime compared with conventional greedy algorithm.

Sparse Poisson regression via mixed-integer optimization.

We present a mixed-integer optimization (MIO) approach to sparse Poisson regression. The MIO approach to sparse linear regression was first proposed in the 1970s, but has recently received renewed attention due to advances in optimization algorithms and computer hardware. In contrast to many sparse estimation algorithms, the MIO approach has the advantage of finding the best subset of explanatory variables with respect to various criterion functions. In this paper, we focus on a sparse Poisson regression that maximizes the weighted sum of the log-likelihood function and the L2-regularization term. For this problem, we derive a mixed-integer quadratic optimization (MIQO) formulation by applying a piecewise-linear approximation to the log-likelihood function. Optimization software can solve this MIQO problem to optimality. Moreover, we propose two methods for selecting a limited number of tangent lines effective for piecewise-linear approximations. We assess the efficacy of our method through computational experiments using synthetic and real-world datasets. Our methods provide better log-likelihood values than do conventional greedy algorithms in selecting tangent lines. In addition, our MIQO formulation delivers better out-of-sample prediction performance than do forward stepwise selection and L1-regularized estimation, especially in low-noise situations.

Local Alignment of DNA Sequence Based on Deep Reinforcement Learning.

Goal: Over the decades, there have been improvements in the sequence alignment algorithm, with significant advances in various aspects such as complexity and accuracy. However, human-defined algorithms have an explicit limitation in view of developmental completeness. This paper introduces a novel local alignment method to obtain optimal sequence alignment based on reinforcement learning. Methods: There is a DQNalign algorithm that learns and performs sequence alignment through deep reinforcement learning. This paper proposes a DQN x-drop algorithm that performs local alignment without human intervention by combining the x-drop algorithm with this DQNalign algorithm. The proposed algorithm performs local alignment by repeatedly observing the subsequences and selecting the next alignment direction until the x-drop algorithm terminates the DQNalign algorithm. This proposed algorithm has an advantage in view of linear computational complexity compared to conventional local alignment algorithms. Results: This paper compares alignment performance (coverage and identity) and complexity for a fair comparison between the proposed DQN x-drop algorithm and the conventional greedy x-drop algorithm. Firstly, we prove the proposed algorithm's superiority by comparing the two algorithms’ computational complexity through numerical analysis. After that, we tested the alignment performance actual HEV and E.coli sequence datasets. The proposed method shows the comparable identity and coverage performance to the conventional alignment method while having linear complexity for the n}{}X parameter. Conclusions: Through this study, it was possible to confirm the possibility of a new local alignment algorithm that minimizes computational complexity without human intervention.

Joint Bayesian and Greedy Recovery for Compressive Sensing

Greedy algorithms are widely used for sparse recovery in compressive sensing. Conventional greedy algorithms employ the inner product vector of signal residual and sensing matrix to determine the support, which is based on the assumption that the indexes of the larger-magnitude entries of the inner product vector are more likely to be contained in the correct supports. However, this assumption may be not valid when the number of measurements is not sufficient, leading to the selection of an incorrect support. To improve the accuracy of greedy recovery, we propose a novel greedy algorithm to recover sparse signals from incomplete measurements. The entries of a sparse signal are modelled by the type-II Laplacian prior, such that the k indexes of the correct support are indicated by the largest k variance hyperparameters of the entries. Based on the proposed model, the supports can be recovered by approximately estimating the hyperparameters via the maximum a posteriori process. Simulation results demonstrate that the proposed algorithm outperforms the conventional greedy algorithms in terms of recovery accuracy, and it exhibits satisfactory recovery speed.

Pilot-Less One-Shot Sparse Coding for Short Packet-Based Machine-Type Communications

This paper presents a novel transmission scheme to support massive machine-type communications (MTC) devices sending very short packets for Internet-of-Things (IoT) applications. The proposed scheme, termed as pilot-less one-shot (PLOS) transmission, does not require the pilot signaling. The key idea behind PLOS is to encode information into the inter-block nonzero positions and intra-block nonzero positions of a sparse vector. In the receiver, we propose a deep neural network-based scheme, referred to as deep learning-based PLOS (DL-PLOS) to recover the nonzero positions of the sparse vector. From the simulations results, we demonstrate that PLOS is effective in the short packet transmission and DL-PLOS outperforms the conventional greedy algorithms.

Low-Complexity Multi-User Detection Based on Gradient Information for Uplink Grant-Free NOMA

Massive machine type communication (mMTC) serves an irreplaceable role in the development process of the Internet of Things (IoT). Because of its characteristics of massive connection and sporadic transmission, compressed sensing (CS) has been applied in joint user activity and data detection in the uplink grant-free non-orthogonal multiple access (NOMA) system. In previous work, greedy iterative-based multi-user detection (MUD) algorithms were developed in mMTC scenarios because of the computational benefit and competitive performance. However, conventional greedy iterative-based MUD algorithms still suffer from high computational complexity due to the process of large-size matrix inversion with the accession of massive devices into the system. In this paper, gradient information is used to address this problem. A low-complexity gradient descent-based gradient pursuit MUD (GDGP-MUD) algorithm is proposed, which uses the gradient information of error function in the process of iteration as a new updating direction, instead of the matrix inversion process. Then, a multi-step quasi-Newton MUD (MSQN-MUD) algorithm is proposed to improve the precision of detection while maintaining low complexity. In the algorithm, high-order information in the process of adjacent iteration is used effectively to update data values more accurately. Moreover, the convergence and complexity analysis of both algorithms are derived. The analysis shows that both proposed algorithms have lower computational consumption than most of the state-of-the-art greedy-based MUD algorithms. It is worth noting that in comparison to most existing CS-based MUD algorithms, the two proposed algorithms do not require the exact user sparsity level and, thus, reduce the dependence on prior knowledge. The numerical experiments demonstrate that the proposed algorithms have better real-time performance than existing greedy-based MUD algorithms with similar symbol error rate performance.

Modal regression based greedy algorithm for robust sparse signal recovery, clustering and classification

Greedy algorithm (GA) is an efficient sparse representation framework with numerous applications in machine learning and computer vision. However, conventional GA methods may fail when applied to grossly corrupted data because they iteratively estimate the sparse signal using least squares regression, which is sensitive to gross corruption and outliers. In this paper, we propose a modal regression based greedy algorithm referred as MROMP (modal regression based orthogonal matching pursuit) to robustly learn the sparse signal from corrupted measurements. Unlike previous GA methods, MROMP is based on sparse modal regression, which has decent robustness to heavy-tailed noise and outliers. To efficiently optimize MROMP, we devise two half-quadratic based algorithms with guaranteed convergence. Our another two contributions are leveraging MROMP to develop a robust subspace clustering method to cluster data lying in a union of subspaces, and a robust pattern classification method to recognize data into the class that they belong to, respectively. The experimental results on both simulated and real datasets demonstrate the efficacy and robustness of MROMP for sparse signal recovery, data clustering and classification, especially for grossly corrupted data.

Cauchy greedy algorithm for robust sparse recovery and multiclass classification

Greedy algorithms have attracted considerable interest for sparse signal recovery (SSR) due to their appealing efficiency and performance recently. However, conventional greedy algorithms utilize the ℓ2 norm based loss function and suffer from severe performance degradation in the presence of gross corruption and outliers. Furthermore, they cannot be directly applied to the recovery of quaternion sparse signals due to the noncommutativity of quaternion multiplication. To alleviate these problems, we propose a robust greedy algorithm referred as Cauchy matching pursuit (CauchyMP) for SSR and extend it for quaternion SSR. By leveraging the Cauchy estimator and generalizing it to the quaternion space to measure the residual error, our method can robustly recover the sparse signal in both real and quaternion space from noisy data corrupted by various severe noises and outliers. To tackle the resulting quaternion optimization problem, we develop an efficient half-quadratic optimization algorithm by introducing two quaternion operators. In addition, we have also devised a CauchyMP based classifier termed CauchyMPC for robust multiclass classification. The experiments on both synthetic and real-world datasets validate the efficacy and robustness of the proposed methods for SSR, block SSR, quaternion SSR and multiclass classification.

A topology optimization method for electric machines and devices through submodular maximization

AbstractThis paper presents a topology optimization method using a greedy algorithm for submodular maximization. This method is based on a shape representation using the normalized Gaussian network. The weight coefficients of Gaussians are discretized to +1/−1, and then their values are greedily inverted. Hence, the computational cost of the present method is relatively smaller than that of evolutionary algorithms. The present method is applied to a magnetic shield optimization problem. It is shown that Pareto solutions can be obtained by the present method. In addition, it can be found from the numerical results that the stochastic greedy algorithm can effectively reduce the computational time compared with the conventional greedy algorithm. As a result, it is shown that a 3‐D optimization problem with over 3000 design variables can be solved within acceptable computational time.

Compressed channel estimation for FDD massive MIMO systems without prior knowledge of sparse channel model

In this study, a new greedy-based algorithm for sparse channel estimation in frequency-division duplexing massive multiple-input multiple-output (MIMO) systems is introduced. The proposed algorithm is able to acquire the channel with no information about the channel model such as the sparsity order, statistical bound on sparsity support, and special features of the channel. In other words, the authors assume that the massive channel is totally unknown and then exploit the inherent property of correlation between measurements and the sensing matrix to estimate the channel, which is available at the user side. By utilising this property, a halting parameter is defined as the halting threshold instead of known prior information assumed in the conventional greedy algorithms. Furthermore, the lower and upper bounds of the halting parameter are obtained that helps the algorithm to take the suitable values of this parameter and by considering the lower bound as the values of the halting parameter, the algorithm can prevent from missing the original channel bins. Simulation results demonstrate that the proposed algorithm outperforms its counterparts in terms of normalised mean square error while it faces a completely unknown massive MIMO channel.

A genetic algorithm based task scheduling system for logistics service robots

The demand for autonomous logistics service robots requires an efficient task scheduling system in order to optimise cost and time for the robot to complete its tasks. This paper presents a Genetic algorithm (GA) based task scheduling system for a ground mobile robot that is able to find a global near-optimal travelling path to complete a logistics task of pick-and-deliver items at various locations. In this study, the chromosome representation and the fitness function of GA is carefully designed to cater for a single load logistics robotic task. Two variants of GA crossover are adopted to enhance the performance of the proposed algorithm. The performance of the scheduling is compared and analysed between the proposed GA algorithms and a conventional greedy algorithm in a virtual map and a real map environments that turns out the proposed GA algorithms outperform the greedy algorithm by 40% to 80% improvement.

GARLM: Greedy Autocorrelation Retrieval Levenberg–Marquardt Algorithm for Improving Sparse Phase Retrieval

The goal of phase retrieval is to recover an unknown signal from the random measurements consisting of the magnitude of its Fourier transform. Due to the loss of the phase information, phase retrieval is considered as an ill-posed problem. Conventional greedy algorithms, e.g., greedy spare phase retrieval (GESPAR), were developed to solve this problem by using prior knowledge of the unknown signal. However, due to the defect of the Gauss–Newton method in the local convergence problem, especially when the residual is large, it is very difficult to use this method in GESPAR to efficiently solve the non-convex optimization problem. In order to improve the performance of the greedy algorithm, we propose an improved phase retrieval algorithm, which is called the greedy autocorrelation retrieval Levenberg–Marquardt (GARLM) algorithm. Specifically, the proposed GARLM algorithm is a local search iterative algorithm to recover the sparse signal from its Fourier transform magnitude. The proposed algorithm is preferred to existing greedy methods of phase retrieval, since at each iteration the problem of minimizing the objective function over a given support is solved by using the improved Levenberg–Marquardt (ILM) method and matrix transform. A local search procedure such as the 2-opt method is then invoked to get the optimal estimation. Simulation results are given to show that the proposed algorithm performs better than the conventional GESPAR algorithm.