arXiv subjects

Minghua Chen

Publications and source records attributed to Minghua Chen.

At least 109 records · Page 6Linked to original sources

arXiv2013

A second-order numerical method for two-dimensional two-sided space fractional convection diffusion equation

Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this paper, we discuss the practical alternating directions implicit method to solve the two-dimensional two-sided space fractional convection diffusion equation on a finite domain. We theoretically prove and numerically verify that the presented finite difference scheme is unconditionally von Neumann stable and second order convergent in both space and time directions.

math.NA↗

arXiv2013

Dynamic Provisioning in Next-Generation Data Centers with On-site Power Production

The critical need for clean and economical sources of energy is transforming data centers that are primarily energy consumers to also energy producers. We focus on minimizing the operating costs of next-generation data centers that can jointly optimize the energy supply from on-site generators and the power grid, and the energy demand from servers as well as power conditioning and cooling systems. We formulate the cost minimization problem and present an offline optimal algorithm. For "on-grid" data centers that use only the grid, we devise a deterministic online algorithm that achieves the best possible competitive ratio of $2-α_{s}$, where $α_{s}$ is a normalized look-ahead window size. For "hybrid" data centers that have on-site power generation in addition to the grid, we develop an online algorithm that achieves a competitive ratio of at most \textmd{\normalsize {\small $\frac{P_{\max} (2-α_{s})}{c_{o}+c_{m}/L} [1+2\frac{P_{\max}-c_{o}}{P_{\max}(1+α_{g})}]$}}, where $α_{s}$ and $α_{g}$ are normalized look-ahead window sizes, $P_{\max}$ is the maximum grid power price, and $L$, $c_{o}$, and $c_{m}$ are parameters of an on-site generator. Using extensive workload traces from Akamai with the corresponding grid power prices, we simulate our offline and online algorithms in a realistic setting. Our offline (resp., online) algorithm achieves a cost reduction of 25.8% (resp., 20.7%) for a hybrid data center and 12.3% (resp., 7.3%) for an on-grid data center. The cost reductions are quite significant and make a strong case for a joint optimization of energy supply and energy demand in a data center. A hybrid data center provides about 13% additional cost reduction over an on-grid data center representing the additional cost benefits that on-site power generation provides over using the grid alone.

cs.DS↗

arXiv2013

Efficient numerical algorithms for three-dimensional fractional partial differential equations

This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional diffusion equation. The second order finite difference scheme is used to discretize the space fractional derivative and the Crank-Nicolson procedure to the time derivative. We theoretically prove and numerically verify that the presented numerical methods are unconditionally stable and second order convergent in both space and time directions. In particular, for the Riesz fractional diffusion equation, the idea of reducing the splitting error is used to further improve the algorithm, and the unconditional stability and convergency are also strictly proved and numerically verified for the improved scheme.

math.NA↗

arXiv2013

Routing for Security in Networks with Adversarial Nodes

We consider the problem of secure unicast transmission between two nodes in a directed graph, where an adversary eavesdrops/jams a subset of nodes. This adversarial setting is in contrast to traditional ones where the adversary controls a subset of links. In particular, we study, in the main, the class of routing-only schemes (as opposed to those allowing coding inside the network). Routing-only schemes usually have low implementation complexity, yet a characterization of the rates achievable by such schemes was open prior to this work. We first propose an LP based solution for secure communication against eavesdropping, and show that it is information-theoretically rate-optimal among all routing-only schemes. The idea behind our design is to balance information flow in the network so that no subset of nodes observe "too much" information. Interestingly, we show that the rates achieved by our routing-only scheme are always at least as good as, and sometimes better, than those achieved by "naïve" network coding schemes (i.e. the rate-optimal scheme designed for the traditional scenario where the adversary controls links in a network rather than nodes.) We also demonstrate non-trivial network coding schemes that achieve rates at least as high as (and again sometimes better than) those achieved by our routing schemes, but leave open the question of characterizing the optimal rate-region of the problem under all possible coding schemes. We then extend these routing-only schemes to the adversarial node-jamming scenarios and show similar results. During the journey of our investigation, we also develop a new technique that has the potential to derive non-trivial bounds for general secure-communication schemes.

cs.IT↗

arXiv2013

Second-order LOD multigrid method for multidimensional Riesz fractional diffusion equation

We propose a locally one dimensional (LOD) finite difference method for multidimensional Riesz fractional diffusion equation with variable coefficients on a finite domain. The numerical method is second-order convergent in both space and time directions, and its unconditional stability is strictly proved. Comparing with the popular first-order finite difference method for fractional operator, the form of obtained matrix algebraic equation is changed from $(I-A)u^{k+1}=u^k+b^{k+1}$ to $(I-{\widetilde A})u^{k+1}=(I+{\widetilde B})u^k+{\tilde b}^{k+1/2}$; the three matrices $A$, ${\widetilde A}$ and ${\widetilde B}$ are all Toeplitz-like, i.e., they have completely same structure and the computational count for matrix vector multiplication is $\mathcal{O}(N {log} N)$; and the computational costs for solving the two matrix algebraic equations are almost the same. The LOD-multigrid method is used to solve the resulting matrix algebraic equation, and the computational count is $\mathcal{O}(N {log} N)$ and the required storage is $\mathcal{O}(N)$, where $N$ is the number of grid points. Finally, the extensive numerical experiments are performed to show the powerfulness of the second-order scheme and the LOD-multigrid method.

math.NA↗

arXiv2012

SHO-FA: Robust compressive sensing with order-optimal complexity, measurements, and bits

Suppose x is any exactly k-sparse vector in R^n. We present a class of sparse matrices A, and a corresponding algorithm that we call SHO-FA (for Short and Fast) that, with high probability over A, can reconstruct x from Ax. The SHO-FA algorithm is related to the Invertible Bloom Lookup Tables recently introduced by Goodrich et al., with two important distinctions - SHO-FA relies on linear measurements, and is robust to noise. The SHO-FA algorithm is the first to simultaneously have the following properties: (a) it requires only O(k) measurements, (b) the bit-precision of each measurement and each arithmetic operation is O (log(n) + P) (here 2^{-P} is the desired relative error in the reconstruction of x), (c) the decoding complexity is O(k) arithmetic operations and encoding complexity is O(n) arithmetic operations, and (d) if the reconstruction goal is simply to recover a single component of x instead of all of x, with significant probability over A this can be done in constant time. All constants above are independent of all problem parameters other than the desired success probability. For a wide range of parameters these properties are information-theoretically order-optimal. In addition, our SHO-FA algorithm works over fairly general ensembles of "sparse random matrices", is robust to random noise, and (random) approximate sparsity for a large range of k. In particular, suppose the measured vector equals A(x+z)+e, where z and e correspond respectively to the source tail and measurement noise. Under reasonable statistical assumptions on z and e our decoding algorithm reconstructs x with an estimation error of O(||z||_2 +||e||_2). The SHO-FA algorithm works with high probability over A, z, and e, and still requires only O(k) steps and O(k) measurements over O(log n)-bit numbers. This is in contrast to the worst-case z model, where it is known O(k log n/k) measurements are necessary.

cs.IT↗

arXiv2012

Second order finite difference approximations for the two-dimensional time-space Caputo-Riesz fractional diffusion equation

In this paper, we discuss the time-space Caputo-Riesz fractional diffusion equation with variable coefficients on a finite domain. The finite difference schemes for this equation are provided. We theoretically prove and numerically verify that the implicit finite difference scheme is unconditionally stable (the explicit scheme is conditionally stable with the stability condition $\frac{τ^γ}{(Δx)^α}+\frac{τ^γ}{(Δy)^β} <C$) and 2nd order convergent in space direction, and $(2-γ)$-th order convergent in time direction, where $γ\in(0,1]$.

math.NA↗

arXiv2012

Optimal Distributed P2P Streaming under Node Degree Bounds

We study the problem of maximizing the broadcast rate in peer-to-peer (P2P) systems under \emph{node degree bounds}, i.e., the number of neighbors a node can simultaneously connect to is upper-bounded. The problem is critical for supporting high-quality video streaming in P2P systems, and is challenging due to its combinatorial nature. In this paper, we address this problem by providing the first distributed solution that achieves near-optimal broadcast rate under arbitrary node degree bounds, and over arbitrary overlay graph. It runs on individual nodes and utilizes only the measurement from their one-hop neighbors, making the solution easy to implement and adaptable to peer churn and network dynamics. Our solution consists of two distributed algorithms proposed in this paper that can be of independent interests: a network-coding based broadcasting algorithm that optimizes the broadcast rate given a topology, and a Markov-chain guided topology hopping algorithm that optimizes the topology. Our distributed broadcasting algorithm achieves the optimal broadcast rate over arbitrary P2P topology, while previously proposed distributed algorithms obtain optimality only for P2P complete graphs. We prove the optimality of our solution and its convergence to a neighborhood around the optimal equilibrium under noisy measurements or without time-scale separation assumptions. We demonstrate the effectiveness of our solution in simulations using uplink bandwidth statistics of Internet hosts.

cs.NI↗

arXiv2012

Analog Network Coding in General SNR Regime

The problem of maximum rate achievable with analog network coding for a unicast communication over a layered wireless relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals received at its input. Recently this problem has been considered under two assumptions: (A) each relay node scales its received signal to the upper bound of its transmit power constraint, (B) the relay nodes in specific subsets of the network operate in the high-SNR regime. We establish that assumption (A), in general, leads to suboptimal end-to-end rate. We also characterize the performance of analog network coding in class of symmetric layered networks without assumption (B). The key contribution of this work is a lemma that states that a globally optimal set of scaling factors for the nodes in a layered relay network that maximizes the end-to-end rate can be computed layer-by-layer. Specifically, a rate-optimal set of scaling factors for the nodes in a layer is the one that maximizes the sum-rate of the nodes in the next layer. This critical insight allows us to characterize analog network coding performance in network scenarios beyond those that can be analyzed using the existing approaches. We illustrate this by computing the maximum rate achievable with analog network coding in one particular layered network, in various communication scenarios.

cs.IT↗

arXiv2012

Analog network coding in general SNR regime: Performance of a greedy scheme

The problem of maximum rate achievable with analog network coding for a unicast communication over a layered relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals received at its input. Recently this problem has been considered under certain assumptions on per node scaling factor and received SNR. Previously, we established a result that allows us to characterize the optimal performance of analog network coding in network scenarios beyond those that can be analyzed using the approaches based on such assumptions. The key contribution of this work is a scheme to greedily compute a lower bound to the optimal rate achievable with analog network coding in the general layered networks. This scheme allows for exact computation of the optimal achievable rates in a wider class of layered networks than those that can be addressed using existing approaches. For the specific case of Gaussian N-relay diamond network, to the best of our knowledge, the proposed scheme provides the first exact characterization of the optimal rate achievable with analog network coding. Further, for general layered networks, our scheme allows us to compute optimal rates within a constant gap from the cut-set upper bound asymptotically in the source power.

cs.IT↗

arXiv2012

Analog Network Coding in General SNR Regime: Performance of Network Simplification

We consider a communication scenario where a source communicates with a destination over a directed layered relay network. Each relay performs analog network coding where it scales and forwards the signals received at its input. In this scenario, we address the question: What portion of the maximum end-to-end achievable rate can be maintained if only a fraction of relay nodes available at each layer are used? We consider, in particular, the Gaussian diamond network (layered network with a single layer of relay nodes) and a class of symmetric layered networks. For these networks we show that each relay layer increases the additive gap between the optimal analog network coding performance with and without network simplification (using k instead of N relays in each layer, k < N) by no more than log(N/k)^2 bits and the corresponding multiplicative gap by no more than a factor of (N/k)^2, asymptotically (in source power). To the best of our knowledge, this work offers the first characterization of the performance of network simplification in general layered amplify-and-forward relay networks. Further, unlike most of the current approximation results that attempt to bound optimal rates either within an additive gap or a multiplicative gap, our results suggest a new rate approximation scheme that allows for the simultaneous computation of additive and multiplicative gaps.

cs.IT↗

arXiv2012

Simple and Effective Dynamic Provisioning for Power-Proportional Data Centers

Energy consumption represents a significant cost in data center operation. A large fraction of the energy, however, is used to power idle servers when the workload is low. Dynamic provisioning techniques aim at saving this portion of the energy, by turning off unnecessary servers. In this paper, we explore how much performance gain can knowing future workload information brings to dynamic provisioning. In particular, we study the dynamic provisioning problem under the cost model that a running server consumes a fixed amount energy per unit time, and develop online solutions with and without future workload information available. We first reveal an elegant structure of the off-line dynamic provisioning problem, which allows us to characterize and achieve the optimal solution in a {}"divide-and-conquer" manner. We then exploit this insight to design three online algorithms with competitive ratios $2-α$, $(e-α)/(e-1)\approx1.58-α/(e-1)$ and $e/(e-1+α)$, respectively, where $0\leqα\leq1$ is the fraction of a critical window in which future workload information is available. A fundamental observation is that \emph{future workload information beyond the critical window will not} \emph{improve dynamic provisioning performance}. Our algorithms are decentralized and are simple to implement. We demonstrate their effectiveness in simulations using real-world traces. We also compare their performance with state-of-the-art solutions.

cs.PF↗

arXiv2012

Secure Compressed Reading in Smart Grids

Smart Grids measure energy usage in real-time and tailor supply and delivery accordingly, in order to improve power transmission and distribution. For the grids to operate effectively, it is critical to collect readings from massively-installed smart meters to control centers in an efficient and secure manner. In this paper, we propose a secure compressed reading scheme to address this critical issue. We observe that our collected real-world meter data express strong temporal correlations, indicating they are sparse in certain domains. We adopt Compressed Sensing technique to exploit this sparsity and design an efficient meter data transmission scheme. Our scheme achieves substantial efficiency offered by compressed sensing, without the need to know beforehand in which domain the meter data are sparse. This is in contrast to traditional compressed-sensing based scheme where such sparse-domain information is required a priori. We then design specific dependable scheme to work with our compressed sensing based data transmission scheme to make our meter reading reliable and secure. We provide performance guarantee for the correctness, efficiency, and security of our proposed scheme. Through analysis and simulations, we demonstrate the effectiveness of our schemes and compare their performance to prior arts.

cs.IT↗

arXiv2011

Amplify-and-Forward in Wireless Relay Networks

A general class of wireless relay networks with a single source-destination pair is considered. Intermediate nodes in the network employ an amplify-and-forward scheme to relay their input signals. In this case the overall input-output channel from the source via the relays to the destination effectively behaves as an intersymbol interference channel with colored noise. Unlike previous work we formulate the problem of the maximum achievable rate in this setting as an optimization problem with no assumption on the network size, topology, and received signal-to-noise ratio. Previous work considered only scenarios wherein relays use all their power to amplify their received signals. We demonstrate that this may not always maximize the maximal achievable rate in amplify-and-forward relay networks. The proposed formulation allows us to not only recover known results on the performance of the amplify-and-forward schemes for some simple relay networks but also characterize the performance of more complex amplify-and-forward relay networks which cannot be addressed in a straightforward manner using existing approaches. Using cut-set arguments, we derive simple upper bounds on the capacity of general wireless relay networks. Through various examples, we show that a large class of amplify-and-forward relay networks can achieve rates within a constant factor of these upper bounds asymptotically in network parameters.

cs.IT↗

arXiv2011

Enabling Multi-level Trust in Privacy Preserving Data Mining

Privacy Preserving Data Mining (PPDM) addresses the problem of developing accurate models about aggregated data without access to precise information in individual data record. A widely studied \emph{perturbation-based PPDM} approach introduces random perturbation to individual values to preserve privacy before data is published. Previous solutions of this approach are limited in their tacit assumption of single-level trust on data miners. In this work, we relax this assumption and expand the scope of perturbation-based PPDM to Multi-Level Trust (MLT-PPDM). In our setting, the more trusted a data miner is, the less perturbed copy of the data it can access. Under this setting, a malicious data miner may have access to differently perturbed copies of the same data through various means, and may combine these diverse copies to jointly infer additional information about the original data that the data owner does not intend to release. Preventing such \emph{diversity attacks} is the key challenge of providing MLT-PPDM services. We address this challenge by properly correlating perturbation across copies at different trust levels. We prove that our solution is robust against diversity attacks with respect to our privacy goal. That is, for data miners who have access to an arbitrary collection of the perturbed copies, our solution prevent them from jointly reconstructing the original data more accurately than the best effort using any individual copy in the collection. Our solution allows a data owner to generate perturbed copies of its data for arbitrary trust levels on-demand. This feature offers data owners maximum flexibility.

cs.DB↗

arXiv2010

Distributed and Optimal Reduced Primal-Dual Algorithm for Uplink OFDM Resource Allocation

Orthogonal Frequency Division Multiplexing (OFDM) is the key component of many emerging broadband wireless access standards. The resource allocation in OFDM uplink, however, is challenging due to heterogeneity of users' Quality of Service requirements, channel conditions, and individual resource constraints. We formulate the resource allocation problem as a non-strictly convex optimization problem, which typically has multiple global optimal solutions. We then propose a reduced primal-dual algorithm, which is distributed, low in computational complexity, and probably globally convergent to a global optimal solution. The performance of the algorithm is studied through a realistic OFDM simulator. Compared with the previously proposed centralized optimal algorithm, our algorithm not only significantly reduces the message overhead but also requires less iterations to converge.

cs.NI↗

arXiv2010

An Adaptive Multi-channel P2P Video-on-Demand System using Plug-and-Play Helpers

We present a multi-channel P2P Video-on-Demand (VoD) system using "plug-and-play" helpers. Helpers are heterogenous "micro-servers" with limited storage, bandwidth and number of users they can serve simultaneously. Our proposed system has the following salient features: (1) it minimizes the server load; (2) it is distributed, and requires little or no maintenance overhead and which can easily adapt to system dynamics; and (3) it is adaptable to varying supply and demand patterns across multiple video channels irrespective of video popularity. Our proposed solution jointly optimizes over helper-user topology, video storage allocation and bandwidth allocation. The combinatorial nature of the problem and the system demand for distributed algorithms makes the problem uniquely challenging. By utilizing Lagrangian decomposition and Markov chain approximation based arguments, we address this challenge by designing two distributed algorithms running in tandem: a primal-dual storage and bandwidth allocation algorithm and a "soft-worst-neighbor-choking" topology-building algorithm. Our scheme provably converges to a near-optimal solution, and is easy to implement in practice. Simulation results validate that the proposed scheme achieves minimum sever load under highly heterogeneous combinations of supply and demand patterns, and is robust to system dynamics of user/helper churn, user/helper asynchrony, and random delays in the network.

cs.NI↗

arXiv2010

TCP Reno over Adaptive CSMA

An interesting distributed adaptive CSMA MAC protocol, called adaptive CSMA, was proposed recently to schedule any strictly feasible achievable rates inside the capacity region. Of particular interest is the fact that the adaptive CSMA can achieve a system utility arbitrarily close to that is achievable under a central scheduler. However, a specially designed transport-layer rate controller is needed for this result. An outstanding question is whether the widely-installed TCP Reno is compatible with adaptive CSMA and can achieve the same result. The answer to this question will determine how close to practical deployment adaptive CSMA is. Our answer is yes and no. First, we observe that running TCP Reno directly over adaptive CSMA results in severe starvation problems. Effectively, its performance is no better than that of TCP Reno over legacy CSMA (IEEE 802.11), and the potentials of adaptive CSMA cannot be realized. Fortunately, we find that multi-connection TCP Reno over adaptive CSMA with active queue management can materialize the advantages of adaptive CSMA. NS-2 simulations demonstrate that our solution can alleviate starvation and achieve fair and efficient rate allocation. Multi-connection TCP can be implemented at either application or transport layer. Application-layer implementation requires no kernel modification, making the solution readily deployable in networks running adaptive CSMA.

cs.NI↗