Joint Placement and Allocation of VNF Nodes with Budget and Capacity Constraints

With the advent of Network Function Virtualization (NFV), network services that traditionally run on proprietary dedicated hardware can now be realized using Virtual Network Functions (VNFs) that are hosted on general-purpose commodity hardware. This new network paradigm offers a great flexibility to Internet service providers (ISPs) for efficiently operating their networks (collecting network statistics, enforcing management policies, etc.). However, introducing NFV requires an investment to deploy VNFs at certain network nodes (called VNF-nodes), which has to account for practical constraints such as the deployment budget and the VNF-node capacity. To that end, it is important to design a joint VNF-nodes placement and capacity allocation algorithm that can maximize the total amount of network flows that are fully processed by the VNF-nodes while respecting such practical constraints. In contrast to most prior work that often neglects either the budget constraint or the capacity constraint, we explicitly consider both of them. We prove that accounting for these constraints introduces several new challenges. Specifically, we prove that the studied problem is not only NP-hard but also non-submodular. To address these challenges, we introduce a novel relaxation method such that the objective function of the relaxed placement subproblem becomes submodular. Leveraging this useful submodular property, we propose two algorithms that achieve an approximation ratio of $\frac{1}{2}(1-1/e)$ and $\frac{1}{3}(1-1/e)$ for the original non-relaxed problem, respectively. Finally, we corroborate the effectiveness of the proposed algorithms through extensive evaluations using trace-driven simulations

The Power of Waiting for More than One Response in Minimizing the Age-of-Information

The Age-of-Information (AoI) has recently been proposed as an important metric for investigating the timeliness performance in information-update systems. Prior studies on AoI optimization often consider a Push model, which is concerned about when and how to "push" (i.e., generate and transmit) the updated information to the user. In stark contrast, in this paper we introduce a new Pull model, which is more relevant for certain applications (such as the real-time stock quotes service), where a user sends requests to the servers to proactively "pull" the information of interest. Moreover, we propose to employ request replication to reduce the AoI. Interestingly, we find that under this new Pull model, replication schemes capture a novel tradeoff between different levels of information freshness and different response times across the servers, which can be exploited to minimize the expected AoI at the user's side. Specifically, assuming Poisson updating process at the servers and exponentially distributed response time, we derive a closedform formula for computing the expected AoI and obtain the optimal number of responses to wait for to minimize the expected AoI. Finally, we conduct numerical simulations to elucidate our theoretical results. Our findings show that waiting for more than one response can significantly reduce the AoI in most scenarios

Dantzig Selector with an Approximately Optimal Denoising Matrix and its Application to Reinforcement Learning

Dantzig Selector (DS) is widely used in compressed sensing and sparse learning for feature selection and sparse signal recovery. Since the DS formulation is essentially a linear programming optimization, many existing linear programming solvers can be simply applied for scaling up. The DS formulation can be explained as a basis pursuit denoising problem, wherein the data matrix (or measurement matrix) is employed as the denoising matrix to eliminate the observation noise. However, we notice that the data matrix may not be the optimal denoising matrix, as shown by a simple counter-example. This motivates us to pursue a better denoising matrix for defining a general DS formulation. We first define the optimal denoising matrix through a minimax optimization, which turns out to be an NPhard problem. To make the problem computationally tractable, we propose a novel algorithm, termed as Optimal Denoising Dantzig Selector (ODDS), to approximately estimate the optimal denoising matrix. Empirical experiments validate the proposed method. Finally, a novel sparse reinforcement learning algorithm is formulated by extending the proposed ODDS algorithm to temporal difference learning, and empirical experimental results demonstrate to outperform the conventional vanilla DS-TD algorithm

Target reconstruction with a reference point scatterer using phaseless far field patterns

An important property of the phaseless far field patterns with incident plane waves is the translation invariance. Thus it is impossible to reconstruct the location of the underlying scatterers. By adding a reference point scatterer into the model, we design a novel direct sampling method using the phaseless data directly. The reference point technique not only overcomes the translation invariance, but also brings a practical phase retrieval algorithm. Based on this, we propose a hybrid method combining the novel phase retrieval algorithm and the classical direct sampling methods. Numerical examples in two dimensions are presented to demonstrate their effectiveness and robustness

Lorentz Force Correction and Radiation Frequency Property of Charged Particles in Magnetic Dipole

By concern of compression of charge density field, the corrected Lorentz force formula and consequent inference is presented. And further radiation frequency property of an individual charge density field in magnetic dipole is analyzed respectively for radiant property of the charged particle and the emitted electromagnetic wave transfer property between the moving radiant source and observer. As results, the behavior and radiation frequency property of the electron beam in magnetic dipole is interpreted upon the individual's behavior and property. At final, the potential application is put forward for wider interest.Comment: 6 Page

Concentrating Electric and Thermal Fields Simultaneously Using Fan-shaped Structure

Recently, considerable attention has been focused on the transformation optics and metamaterial due to their fascinating phenomena and potential applications. Concentrator is one of the most representative ones, which however is limited in single physical domain. Here we propose and give the experimental demonstration of bifunctional concentrator that can concentrate electric and thermal fields into a given region simultaneously while keeping the external fields undistorted. Fan-shaped structure composed of alternating wedges made of two kinds of natural materials is proposed to achieve this goal. The simulation and experimental results show good agreement, thereby confirming the feasibility of our scheme

Exhaustion of isoperimetric regions in asymptotically hyperbolic manifolds with scalar curvature R≥−6R\geq -6

In this paper, aimed at exploring the fundamental properties of isoperimetric region in $3$-manifold $(M^3,g)$ which is asymptotic to Anti-de Sitter-Schwarzschild manifold with scalar curvature $R\geq -6$, we prove that connected isoperimetric region $\{D_i\}$ with $\mathcal{H}_g ^3(D_i)\geq \delta_0>0$ cannot slide off to the infinity of $(M^3,g)$ provided that $(M^3,g)$ is not isometric to the hyperbolic space. Furthermore, we prove that isoperimetric region $\{D_i\}$ with topological sphere $\{\partial D_i\}$ as boundary is exhausting regions of $M$ if Hawking mass $m_H(\partial D_i)$ has uniform bound. In the case of exhausting isoperimetric region, we obtain a formula on expansion of isoperimetric profile in terms of renormalized volume.Comment: To appear in CA

Providing Wireless Coverage to High-rise Buildings Using UAVs

Unmanned aerial vehicles (UAVs) can be used as aerial wireless base stations when cellular networks go down. Prior studies on UAV-based wireless coverage typically consider an Air-to-Ground path loss model, which assumes that the users are outdoor and they are located on a 2D plane. In this paper, we propose using a single UAV to provide wireless coverage for indoor users inside a high-rise building under disaster situations (such as earthquakes or floods), when cellular networks are down. First, we present a realistic Outdoor-Indoor path loss model and describe the tradeoff introduced by this model. Then, we study the problem of efficient UAV placement, where the objective is to minimize the total transmit power required to cover the entire high-rise building. The formulated problem is non-convex and is generally difficult to solve. To that end, we consider two cases of practical interest and provide the efficient solutions to the formulated problem under these cases. In the first case, we aim to find the minimum transmit power such that an indoor user with the maximum path loss can be covered. In the second case, we assume that the locations of indoor users are symmetric across the dimensions of each floor.Comment: 6 pages, 5 figure

Phaseless inverse source scattering problem: phase retrieval, uniqueness and direct sampling methods

Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the underlying sources. Furthermore, the phaseless far field pattern is also invariant if the source is multiplied by any complex number with modulus one. Therefore, the source can not be uniquely determined, even the multifrequency phaseless far field patterns are considered. By adding a reference point source into the model, we propose a simple and stable phase retrieval method and establish several uniqueness results with phaseless far field data. We proceed to introduce a novel direct sampling method for shape and location reconstruction of the source by using broadband sparse phaseless data directly. We also propose a combination method with the novel phase retrieval algorithm and the classical direct sampling methods with phased data. Numerical examples in two dimensions are also presented to demonstrate their feasibility and effectiveness.Comment: arXiv admin note: text overlap with arXiv:1805.0803

Throughput-optimal Scheduling in Multi-hop Wireless Networks without Per-flow Information

In this paper, we consider the problem of link scheduling in multi-hop wireless networks under general interference constraints. Our goal is to design scheduling schemes that do not use per-flow or per-destination information, maintain a single data queue for each link, and exploit only local information, while guaranteeing throughput optimality. Although the celebrated back-pressure algorithm maximizes throughput, it requires per-flow or per-destination information. It is usually difficult to obtain and maintain this type of information, especially in large networks, where there are numerous flows. Also, the back-pressure algorithm maintains a complex data structure at each node, keeps exchanging queue length information among neighboring nodes, and commonly results in poor delay performance. In this paper, we propose scheduling schemes that can circumvent these drawbacks and guarantee throughput optimality. These schemes use either the readily available hop-count information or only the local information for each link. We rigorously analyze the performance of the proposed schemes using fluid limit techniques via an inductive argument and show that they are throughput-optimal. We also conduct simulations to validate our theoretical results in various settings, and show that the proposed schemes can substantially improve the delay performance in most scenarios.Comment: To appear in IEEE/ACM Transactions on Networking. A preliminary version of this work was presented at IEEE WiOpt 201