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We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. To prevent OGA from overfitting, we introduce a high-dimensional Akaike’s information criterion (HDAIC) to determine the number of OGA iterations. A key contribution of this work is to show that OGA, used in conjunction with HDAIC, can achieve the optimal convergence rate without knowledge of how sparse the underlying high-dimensional model is.

The combination of unmanned aerial vehicles (UAVs) and mobile edge computing (MEC) technology breaks through the limitations of traditional terrestrial communications. The effective line-of-sight channel provided by UAVs can greatly improve the communication quality between edge servers and mobile devices (MDs). To further enhance the Quality-of-Service (QoS) of MEC systems, a multi-UAV-enabled MEC system model is designed. In the proposed model, UAVs are regarded as edge servers to offer computing services for MDs, aiming to minimize the average task response time by jointly optimizing UAV deployment and computation offloading. Based on the problem definition, a two-layer joint optimization method (PSO-GA-G) is proposed. First, the outer layer utilizes a Particle Swarm Optimization algorithm combined with Genetic Algorithm operators (PSO-GA) to optimize UAV deployment. Next, the inner layer adopts a greedy algorithm to optimize computation offloading. The extensive simulation experiments verify the feasibility and effectiveness of the proposed PSO-GA-G. The results show that the PSO-GA-G can achieve a lower average task response time than the other three baselines.

Greedy algorithms are a fundamental class of mathematics and computer science algorithms, defined by their iterative approach of making locally optimal decisions to approximate global optima. In this review, we focus on two greedy algorithms. First, we examine the relaxed greedy algorithm in the context of dictionaries in Hilbert spaces, analyzing the optimality of the definition of this algorithm. Next, we provide a general overview of the thresholding greedy algorithm and the Chebyshev thresholding greedy algorithm, with particular attention to their applications to bases in p -Banach spaces with 0 < p ≤ 1 . In both cases, we conclude by posing several questions for future research.

Cloud RAN, a novel architecture for modern mobile networks, relocates processing units from antenna to distant data centers. This shift introduces the challenge of ensuring low latency for the periodic messages exchanged between antennas and their respective processing units. In this study, we tackle the problem of devising an efficient periodic message assignment scheme under the constraints of fixed message size and period without contention nor buffering. We address this problem by modeling it on a common network topology, wherein contention arises from a single shared link servicing multiple antennas. While reminiscent of coupled task scheduling, the introduction of periodicity adds a unique dimension to the problem. We study how the problem behaves with regard to the load of the shared link, and we focus on proving that, for load as high as possible, a solution always exists and it can be found in polynomial time. The main contributions of this article are two polynomial time algorithms, which find a solution for messages of any size and load at most 2/5 or for messages of size one and load at most ϕ-1, the golden ratio conjugate. We also prove that a randomized greedy algorithm finds a solution on almost all instances with high probability, shedding light on the effectiveness of greedy algorithms in practical applications.

We address the solution of large-scale Bayesian optimal experimental design (OED) problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields. The OED problem seeks to find sensor locations that maximize the expected information gain (EIG) in the solution of the underlying Bayesian inverse problem. Computation of the EIG is usually prohibitive for PDE-based OED problems. To make the evaluation of the EIG tractable, we approximate the (PDE-based) parameter-to-observable map with a derivative-informed projected neural network (DIPNet) surrogate, which exploits the geometry, smoothness, and intrinsic low-dimensionality of the map using a small and dimension-independent number of PDE solves. The surrogate is then deployed within a greedy algorithm-based solution of the OED problem such that no further PDE solves are required. We analyze the EIG approximation error in terms of the generalization error of the DIPNet and show they are of the same order. Finally, the efficiency and accuracy of the method are demonstrated via numerical experiments on OED problems governed by inverse scattering and inverse reactive transport with up to 16,641 uncertain parameters and 100 experimental design variables, where we observe up to three orders of magnitude speedup relative to a reference double loop Monte Carlo method.

This paper focuses on the identification of piecewise-linear Wiener systems alone with multiple inputs, unknown time-delays and system orders in input channels. The parameters and time-delays are jointly estimated by the proposed Householder transformation-based greedy orthogonal least squares (H-GOLS) algorithm. With the help of greedy selection, this algorithm derives the sparse solution. The Householder QR decomposition is employed to reduce the ill-conditioning of the least squares problem, which frequently appears in nonlinear systems. Then we use the Bayesian information criterion to choose the optimal sparsity level for order estimation. Numerical experiments show that the H-GOLS algorithm is more accurate and easier to implement than the LASSO algorithm, which makes it an attractive alternative to identifying sparse Wiener systems within limited data.

Arising from practical problems such as in sensor placement and influence maximization in social network, submodular and non-submodular maximization on the integer lattice has attracted much attention recently. In this work, we consider the problem of maximizing the sum of a monotone non-negative diminishing return submodular (DR-submodular) function and a supermodular function on the integer lattice subject to a cardinality constraint. By exploiting the special combinatorial structures in the problem, we introduce a decreasing threshold greedy algorithm with a binary search as its subroutine to solve the problem. To avoid introducing the diminishing return ratio and submodularity ratio of the objective function, we generalize the total curvatures of submodular functions and supermodular functions to the integer lattice version. We show that our algorithm has a constant approximation ratio parameterized by the new introduced total curvatures on integer lattice with a polynomial query complexity.

We study weights for the thresholding greedy algorithm, aiming to extend previous work on sequential weights ς on N to weights ω on P ( N ) . We revisit major results on weighted greedy-type bases in this new setting including characterizations of ω -(almost) greedy bases and the equivalence between ω -semi-greedy bases and ω -almost greedy bases. Some new results are encountered along the way. For example, we show that there exists an ω -greedy unconditional basis that is not ς -almost greedy for any weight sequence ς . Moreover, a basis is unconditional if and only if it is ω -greedy for some weight ω . Similarly, a basis is quasi-greedy if and only if it is ω -almost greedy for some weight ω .

We address the sensor selection problem where linear measurements under correlated noise are gathered at the selected nodes to estimate the unknown parameter. Since finding the best subset of sensor nodes that minimizes the estimation error requires a prohibitive computational cost especially for a large number of nodes, we propose a greedy selection algorithm that uses the log-determinant of the inverse estimation error covariance matrix as the metric to be maximized. We further manipulate the metric by employing the QR and LU factorizations to derive a simple analytic rule which enables an efficient selection of one node at each iteration in a greedy manner. We also make a complexity analysis of the proposed algorithm and compare with different selection methods, leading to a competitive complexity of the proposed algorithm. For performance evaluation, we conduct numerical experiments using randomly generated measurements under correlated noise and demonstrate that the proposed algorithm achieves a good estimation accuracy with a reasonable selection complexity as compared with the previous novel selection methods.

The autonomous task success of an unmanned aerial vehiclel (UAV) or its military specialization called the unmanned combat aerial vehicle (UCAV) has a direct relationship with the planned path. However, planning a path for a UAV or UCAV system requires solving a challenging problem optimally by considering the different objectives about the enemy threats protecting the battlefield, fuel consumption or battery usage and kinematic constraints on the turning maneuvers. Because of the increasing demands to the UAV systems and game-changing roles played by them, developing new and versatile path planning algorithms become more critical and urgent. In this study, a greedy algorithm named as the Back-and-Forth (BaF) was designed and introduced for solving the path planning problem. The BaF algorithm gets its name from the main strategy where a heuristic approach is responsible to generate two predecessor paths, one of which is calculated from the start point to the target point, while the other is calculated in the reverse direction, and combines the generated paths for utilizing their advantageous line segments when obtaining more safe, short and maneuverable path candidates. The performance of the BaF was investigated over three battlefield scenarios and twelve test cases belonging to them. Moreover, the BaF was integrated into the workflow of a well-known meta-heuristic, artificial bee colony (ABC) algorithm, and detailed experiments were also carried out for evaluating the possible contribution of the BaF on the path planning capabilities of another technique. The results of the experiments showed that the BaF algorithm is able to plan at least promising or generally better paths with the exact consistency than other tested meta-heuristic techniques and runs nine or more times faster as validated through the comparison between the BaF and ABC algorithms. The results of the experiments further proved that the integration of the BaF boosts the performance of the ABC and helps it to outperform all of fifteen competitors for nine of twelve test cases.