Energy Efficient Error Resilient Multiplier Using Low-power Compressors

The approximate hardware design can save huge energy at the cost of errors incurred in the design. This article proposes the approximate algorithm for low-power compressors, utilized to build approximate multiplier with low energy and acceptable error profiles. This article presents two design approaches (DA1 and DA2) for higher bit size approximate multipliers. The proposed multiplier of DA1 have no propagation of carry signal from LSB to MSB, resulted in a very high-speed design. The increment in delay, power, and energy are not exponential with increment of multiplier size ( n ) for DA1 multiplier. It can be observed that the maximum combinations lie in the threshold Error Distance of 5% of the maximum value possible for any particular multiplier of size n . The proposed 4-bit DA1 multiplier consumes only 1.3 fJ of energy, which is 87.9%, 78%, 94%, 67.5%, and 58.9% less when compared to M1, M2, LxA, MxA, accurate designs respectively. The DA2 approach is recursive method, i.e., n -bit multiplier built with n/2-bit sub-multipliers. The proposed 8-bit multiplication has 92% energy savings with Mean Relative Error Distance (MRED) of 0.3 for the DA1 approach and at least 11% to 40% of energy savings with MRED of 0.08 for the DA2 approach. The proposed multipliers are employed in the image processing algorithm of DCT, and the quality is evaluated. The standard PSNR metric is 55 dB for less approximation and 35 dB for maximum approximation.

An analysis between exact and approximate algorithms for the k-center problem in graphs

<span lang="EN-US">This research focuses on the k-center problem and its applications. Different methods for solving this problem are analyzed. The implementations of an exact algorithm and of an approximate algorithm are presented. The source code and the computation complexity of these algorithms are presented and analyzed. The multitasking mode of the operating system is taken into account considering the execution time of the algorithms. The results show that the approximate algorithm finds solutions that are not worse than two times optimal. In some case these solutions are very close to the optimal solutions, but this is true only for graphs with a smaller number of nodes. As the number of nodes in the graph increases (respectively the number of edges increases), the approximate solutions deviate from the optimal ones, but remain acceptable. These results give reason to conclude that for graphs with a small number of nodes the approximate algorithm finds comparable solutions with those founds by the exact algorithm.</span>

A Novel Mathematical Model for Radio Mean Square Labeling Problem

A radio mean square labeling of a connected graph is motivated by the channel assignment problem for radio transmitters to avoid interference of signals sent by transmitters. It is an injective map h from the set of vertices of the graph G to the set of positive integers N , such that for any two distinct vertices x , y , the inequality d x , y + h x 2 + h y 2 / 2 ≥ dim G + 1 holds. For a particular radio mean square labeling h , the maximum number of h v taken over all vertices of G is called its spam, denoted by rmsn h , and the minimum value of rmsn h taking over all radio mean square labeling h of G is called the radio mean square number of G , denoted by rmsn G . In this study, we investigate the radio mean square numbers rmsn P n and rmsn C n for path and cycle, respectively. Then, we present an approximate algorithm to determine rmsn G for graph G . Finally, a new mathematical model to find the upper bound of rmsn G for graph G is introduced. A comparison between the proposed approximate algorithm and the proposed mathematical model is given. We also show that the computational results and their analysis prove that the proposed approximate algorithm overcomes the integer linear programming model (ILPM) according to the radio mean square number. On the other hand, the proposed ILPM outperforms the proposed approximate algorithm according to the running time.

Stochastic Approximate Algorithms for Uncertain Constrained K-Means Problem

The k-means problem has been paid much attention for many applications. In this paper, we define the uncertain constrained k-means problem and propose a (1+ϵ)-approximate algorithm for the problem. First, a general mathematical model of the uncertain constrained k-means problem is proposed. Second, the random sampling properties of the uncertain constrained k-means problem are studied. This paper mainly studies the gap between the center of random sampling and the real center, which should be controlled within a given range with a large probability, so as to obtain the important sampling properties to solve this kind of problem. Finally, using mathematical induction, we assume that the first j−1 cluster centers are obtained, so we only need to solve the j-th center. The algorithm has the elapsed time O((1891ekϵ2)8k/ϵnd), and outputs a collection of size O((1891ekϵ2)8k/ϵn) of candidate sets including approximation centers.

Computing Simplicial Depth by Using Importance Sampling Algorithm and Its Application

Simplicial depth (SD) plays an important role in discriminant analysis, hypothesis testing, machine learning, and engineering computations. However, the computation of simplicial depth is hugely challenging because the exact algorithm is an NP problem with dimension d and sample size n as input arguments. The approximate algorithm for simplicial depth computation has extremely low efficiency, especially in high-dimensional cases. In this study, we design an importance sampling algorithm for the computation of simplicial depth. As an advanced Monte Carlo method, the proposed algorithm outperforms other approximate and exact algorithms in accuracy and efficiency, as shown by simulated and real data experiments. Furthermore, we illustrate the robustness of simplicial depth in regression analysis through a concrete physical data experiment.

Towards Optimal Parallelism-Aware Service Chaining and Embedding

<div>Emerging 5G technologies can significantly reduce end-to-end service latency for applications requiring strict quality of service (QoS). With network function virtualization (NFV), to complete a client’s request from those applications, the client’s data can sequentially go through multiple service functions (SFs) for processing/analysis but introduce additional processing delay. To reduce the processing delay from the serially-running SFs, network function parallelism (NFP) that allows multiple SFs to run in parallel is introduced. In this work, we study how to apply NFP into the SF chaining and embedding process such that the latency, including processing and propagation delays, can be jointly minimized. We introduce a novel augmented graph to address the parallel relationship constraint among the required SFs. Considering parallel relationship constraints, we propose a novel problem called parallelism-aware service function chaining and embedding (PSFCE). For this problem, we propose a near-optimal maximum parallel block gain (MPBG) first optimization algorithm when computing resources at each physical node are enough to host the required SFs. When computing resources are limited, we propose a logarithm-approximate algorithm, called parallelism-aware SFs deployment (PSFD), to jointly optimize processing and propagation delays. We conduct extensive simulations on multiple network scenarios to evaluate the performances of our schemes. Accordingly, we find that (i) MPBG is near-optimal, (ii) the optimization of end-to-end service latency largely depends on the processing delay in small networks and is impacted more by the propagation delay in large networks, and (iii) PSFD outperforms the schemes directly extended from existing works regarding end-to-end latency.</div>

Towards Optimal Parallelism-Aware Service Chaining and Embedding

<div>Emerging 5G technologies can significantly reduce end-to-end service latency for applications requiring strict quality of service (QoS). With network function virtualization (NFV), to complete a client’s request from those applications, the client’s data can sequentially go through multiple service functions (SFs) for processing/analysis but introduce additional processing delay. To reduce the processing delay from the serially-running SFs, network function parallelism (NFP) that allows multiple SFs to run in parallel is introduced. In this work, we study how to apply NFP into the SF chaining and embedding process such that the latency, including processing and propagation delays, can be jointly minimized. We introduce a novel augmented graph to address the parallel relationship constraint among the required SFs. Considering parallel relationship constraints, we propose a novel problem called parallelism-aware service function chaining and embedding (PSFCE). For this problem, we propose a near-optimal maximum parallel block gain (MPBG) first optimization algorithm when computing resources at each physical node are enough to host the required SFs. When computing resources are limited, we propose a logarithm-approximate algorithm, called parallelism-aware SFs deployment (PSFD), to jointly optimize processing and propagation delays. We conduct extensive simulations on multiple network scenarios to evaluate the performances of our schemes. Accordingly, we find that (i) MPBG is near-optimal, (ii) the optimization of end-to-end service latency largely depends on the processing delay in small networks and is impacted more by the propagation delay in large networks, and (iii) PSFD outperforms the schemes directly extended from existing works regarding end-to-end latency.</div>

QoS Correlation-based Service Composition Algorithm for Multi-constraint Optimal Path

With the development of network service integration, in order to obtain a better quality of service (QoS) guarantee, In this Paper,We consider the characteristics of integrated network service composition and correlation, this paper proposes a approximate algorithm based on multi-constraint optimal path selection (MCOPS). We analyses the QoS correlation criteria, correlation ratios, and Skyline algorithms to calculate the optimal path by dynamic programming, record the path nodes, and obtain the optimal service composition path that meets the user's demand. Simulation results demonstrate the good performance of the proposed algorithm in both the average calculation time and the solution path quality.

The Power of the Weighted Sum Scalarization for Approximating Multiobjective Optimization Problems

We determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of approximation that is specifically tailored to the multiobjective case and its inherent trade-offs between different objectives. For minimization problems, we provide an efficient algorithm that computes an approximation of a multiobjective problem by using an exact or approximate algorithm for its weighted sum scalarization. In case that an exact algorithm for the weighted sum scalarization is used, this algorithm comes arbitrarily close to the best approximation quality that is obtainable by supported solutions – both with respect to the common notion of approximation and with respect to the new multi-factor notion. Moreover, the algorithm yields the currently best approximation results for several well-known multiobjective minimization problems. For maximization problems, however, we show that a polynomial approximation guarantee can, in general, not be obtained in more than one of the objective functions simultaneously by supported solutions.

Uniform error estimates for nonequispaced fast Fourier transforms

In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. So far, various window functions have been used and new window functions have recently been proposed. We present novel error estimates for NFFT with compactly supported, continuous window functions and derive rules for convenient choice from the parameters involved in NFFT. The error constant of a window function depends mainly on the oversampling factor and the truncation parameter.