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Addressing non-convexity plays a fundamental role in solving the optimal electricity-gas flow models. In this paper, an improved spatial branch-and-bound algorithm is proposed to solve the non-convex problem, which is formulated as a mixed-integer bilinear programming, for its exact solution. The core of the algorithm is to divide the non-convex model into convex and small sub-models by branching on specific continuous variables, so that the non-convex problem can be equivalent to a rooted tree for exploration. The exactness of the algorithm is guaranteed by the same criterion as the classical branch-and-bound algorithm. To alleviate the computational burden, a novel two-stage spatial branching strategy is developed to improve the effectiveness and efficiency of the branching operations. The performance of the proposed algorithm is verified on two integrated electricity-gas systems with different sizes. Numerical results demonstrate that our method achieves a balance among feasibility, optimality, and efficiency. The comparison with another 6 convexification-based methods, 3 state-of-the-art non-convex optimization solvers, and 2 spatial branch-and-bound algorithms with classical branching rules further shows the superiority of our algorithm. [ABSTRACT FROM AUTHOR]

Nonlinear optimization problems with dynamical parameters are widely arising in many practical scientific and engineering applications, and various computational models are presented for solving them under the hypothesis of short-time invariance. To eliminate the large lagging error in the solution of the inherently dynamic nonlinear optimization problem, the only way is to estimate the future unknown information by using the present and previous data during the solving process, which is termed the future dynamic nonlinear optimization (FDNO) problem. In this paper, to suppress noises and improve the accuracy in solving FDNO problems, a novel noise-tolerant neural (NTN) algorithm based on zeroing neural dynamics is proposed and investigated. In addition, for reducing algorithm complexity, the quasi-Newton Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is employed to eliminate the intensively computational burden for matrix inversion, termed NTN-BFGS algorithm. Moreover, theoretical analyses are conducted, which show that the proposed algorithms are able to globally converge to a tiny error bound with or without the pollution of noises. Finally, numerical experiments are conducted to validate the superiority of the proposed NTN and NTN-BFGS algorithms for the online solution of FDNO problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the coordinated multipoint (CoMP) transmission design for the downlink cloud radio access network (Cloud-RAN). Our design aims to optimize the set of remote radio heads (RRHs) serving each user and the precoding and transmission power to minimize the total transmission power while maintaining the fronthaul capacity and users' quality-of-service (QoS) constraints. The fronthaul capacity constraint involves a nonconvex and discontinuous function that renders the optimal exhaustive search method unaffordable for large networks. To address this challenge, we propose two low-complexity algorithms. The first pricing-based algorithm solves the underlying problem through iteratively tackling a related pricing problem while appropriately updating the pricing parameter. In the second iterative linear-relaxed algorithm, we directly address the fronthaul constraint function by iteratively approximating it with a suitable linear form using a conjugate function and solving the corresponding convex problem. For performance evaluation, we also compare our proposed algorithms with two existing algorithms in the literature. Finally, extensive numerical results are presented, which illustrate the convergence of our proposed algorithms and confirm that our algorithms significantly outperform the state-of-the-art existing algorithms. [ABSTRACT FROM PUBLISHER]

Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods that rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC, and root-MUSIC, are some of the most widely used algorithms to solve these problems. As a common feature, these methods require both a priori knowledge of the number of sources and an estimate of the noise subspace. Both requirements are complicating factors to the practical implementation of the algorithms and, when not satisfied exactly, can potentially lead to severe errors. In this paper, we propose a new localization criterion based on the algebraic structure of the noise subspace that is described for the first time to the best of our knowledge. Using this criterion and the relationship between the source localization problem and the problem of computing the greatest common divisor (GCD), or more practically approximate GCD, for polynomials, we propose two algorithms, which adaptively learn the number of sources and estimate their locations. Simulation results show a significant improvement over root-MUSIC in challenging scenarios such as closely located sources, both in terms of detection of the number of sources and their localization over a broad and practical range of signal-to-noise ratios. Furthermore, no performance sacrifice in simple scenarios is observed. [ABSTRACT FROM AUTHOR]

The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use approximations that are not valid for an unbalanced power distribution system, or apply relaxation techniques to the nonlinear power flow equations that do not guarantee a feasible power flow solution. In this paper, we propose scalable D-OPF algorithms that simultaneously achieve optimal and feasible solutions by solving multiple iterations of approximate, or relaxed, D-OPF subproblems of low complexity. The first algorithm is based on a successive linear approximation of the nonlinear power flow equations around the current operating point, where the D-OPF solution is obtained by solving multiple iterations of a linear programming (LP) problem. The second algorithm is based on the relaxation of the nonlinear power flow equations as conic constraints together with directional constraints, which achieves optimal and feasible solutions over multiple iterations of a second-order cone programming (SOCP) problem. It is demonstrated that the proposed algorithms are able to reach an optimal and feasible solution while significantly reducing the computation time as compared to an equivalent NLP D-OPF model for the same distribution system. [ABSTRACT FROM AUTHOR]

We consider a generalization of both the classic Steiner tree problem and the terminal Steiner tree problem. Given a complete graph G = (V,E) with a metric cost function c:E \rightarrow \BBQ_ \geq and two proper subsets R \subset V and R^\prime \subseteq R, a partial-terminal Steiner tree is a Steiner tree which contains all vertices in \it R such that all vertices in R^\prime must be leaves. The partial-terminal Steiner tree problem is to find a partial-terminal Steiner tree of the minimum cost in G. The previously best-known approximation ratio of the problem is 2\rho, where \bf \rho is the approximation ratio of the Steiner tree problem. In this paper, we improve the ratio from 2\rho to 2\rho - \rho \over 3\rho - 2 - f, where f is a non-negative function whose value is between 0 and \rho - \rho \over 3\rho - 2. [ABSTRACT FROM AUTHOR]

It is of central interest in information theory to determine whether a given vector in the entropy space is an almost entropic vector. This problem can be answered if all the information inequalities are known, but this is an extremely challenging problem. On the other hand, we can establish that a given vector is an entropy vector if we can show the existence of distribution such that the corresponding entropy vector is the same as the given vector. However, there is no known algorithm to solve this problem. Only for the simplest case of binary entropy vectors, an algorithm is known to solve this problem. In this paper, we present a recursive algorithm to determine whether a given vector is a quasi-uniform entropy vector and, if it is, to return a consistent quasi-uniform distribution. We also present two applications of the recursive procedure: (i) to generate all quasi-uniform distributions motivated by the problem of finding the smallest quasi-uniform distribution such that its entropy vector violates the well known Ingleton inequality and (ii) to obtain an entropy vector (not necessarily quasi-uniform) near to a target vector in the entropy space for random variables with given alphabet size. [ABSTRACT FROM AUTHOR]

The minimum dominating set (MDS) of the network is a node subset of smallest size that every node in the network is either in this subset or is adjacent to one or more nodes of this subset. MDS has found wide applications, ranging from network monitoring, routing, to epidemic control, and text processing. However, the majority of existing studies on MDS problem are confined to single networks. In real world, more and more complex systems consist of a set of elements linked up by different types of connections, which are best modeled as multiplex networks with interacting network layers. Though vastly important, the MDS of the multiplex networks has not yet been formally defined and its application and identification remain open issues. In this article, we present the definition of the MDS of the multiplex network and show some of its possible applications. For solving the MDS problem of the multiplex network, we built a spin-glass model and solve it through the belief-propagation (BP) equations under the replica symmetry mean-field theory. As a consequence, we can predict the relative size of the MDS of the multiplex network theoretically and we can propose a BP-guided decimation algorithm to construct an approximate optimal dominating set in practice. Then the algorithm is improved in both accuracy and efficiency by embedding a novel multiplex network-oriented leaf-removal strategy. The effectiveness of the proposed algorithms is finally verified by comparing with other methods on a number of the multiplex network examples. [ABSTRACT FROM AUTHOR]

We study the problem of visually monitoring a set of points on a 2.5D terrain using an unmanned aerial vehicle (UAV) with a downward-facing camera. The goal is to find a tour of minimum length for the UAV offline to visually inspect all points of interest. Varying terrain and limited field of view of the camera restrict the visibility of the UAV and can create obstacles in the flight path, making the problem challenging. The problem is NP-hard and generalizes the traveling salesperson problem (TSP). We present several algorithms to solve this problem. Our main theoretical contribution is a constant-factor approximation algorithm (assuming fixed parameters for the terrain). We also present a practical algorithm that uses the solution to a generalized TSP (GTSP) subinstance. We benchmark the GTSP-based algorithm using a branch-and-cut integer linear programming formulation and find that the proposed algorithm scales to much larger instances and is computationally fast. We also show proof-of-concept using field deployment of a UAV to visually monitor points of interest in the environment. [ABSTRACT FROM AUTHOR]

Approximate Nearest Neighbor Search (ANNS) is a fundamental problem in many areas of machine learning and data mining. During the past decade, numerous hashing algorithms are proposed to solve this problem. Every proposed algorithm claims to outperform Locality Sensitive Hashing (LSH), which is the most popular hashing method. However, the evaluation of these hashing article was not thorough enough, and the claim should be re-examined. If implemented correctly, almost all the hashing methods will have their performance improved as the code length increases. However, many existing hashing article only report the performance with the code length shorter than 128. In this article, we carefully revisit the problem of search-with-a-hash-index and analyze the pros and cons of two popular hash index search procedures. Then we proposed a simple but effective novel hash index search approach and made a thorough comparison of eleven popular hashing algorithms. Surprisingly, the random-projection-based Locality Sensitive Hashing ranked the first, which is in contradiction to the claims in all the other 10 hashing article. Despite the extreme simplicity of random-projection-based LSH, our results show that the capability of this algorithm has been far underestimated. For the sake of reproducibility, all the codes used in the article are released on GitHub, which can be used as a testing platform for a fair comparison between various hashing algorithms. [ABSTRACT FROM AUTHOR]

Mobile edge computing (MEC) is leveraged to reduce the latency for the computation-intensive and latency-critical tasks offloaded from wireless devices and Internet of Things Devices (IoTDs). Unmanned aerial vehicles (UAVs) have attracted much attention from both academia and industry attributed to high mobility, high flexibility, and high maneuverability of UAVs. In this article, a novel UAV-assisted MEC architecture is proposed to provision services to IoTDs, where a UAV provides both communication and computing services or works as a relay node. We then formulate the joint computation offloading, spectrum resource allocation, computation resource allocation, and UAV placement (Joint-CAP) problem in the UAV-MEC network to minimize the operation cost of provisioning IoTDs. Since the Joint-CAP problem is a mixed integer non-linear programming problem and NP-hard, we decompose it into two sub-problems and solve the sub-problems sequentially. Then, we propose a (1 + ε)-approximation algorithm, named AA-CAP, to solve the Joint-CAP problem, and the performance of the AA-CAP algorithm is demonstrated to be superior to the baseline algorithms via simulations. [ABSTRACT FROM AUTHOR]

The future 5G network is expected to provide throughput 1000 times and spectrum efficiency 10 times those of the current 4G network. In-band full-duplex (IBFD) is a promising technique for 5G that can conceivably improve spectrum efficiency. Drone-mounted base stations (DBSs) provide high mobility and high flexibility, and leveraging DBSs to provision services to UEs can facilitate the quality of service of the wireless network and enlarge the coverage area. Therefore, the throughput and the spectrum efficiency can be improved by leveraging IBFD-enabled DBSs. We formulate the drone-mounted base station placement with IBFD communications (DBSP-IBFD) problem, which consists of two sub-problems: the joint bandwidth, power allocation and UE association (joint-BPU) problem and the DBS placement problem. We first propose an approximate algorithm to solve the joint-BPU problem that provides guaranteed performance. Then, an exhaustive search method is employed to obtain the optimal locations for DBSs. After that, we propose a $\frac{1}{2}(1-\frac{1}{2^{l}})$ -approximation algorithm to solve the DBSP-IBFD problem, where $l$ is the number of simulation runs. Simulation results have demonstrated that the throughput of the proposed approximate algorithm is superior to benchmark algorithms in solving the DBSP-IBFD problem. [ABSTRACT FROM AUTHOR]