Algorithm Implementation Issues Research Articles

Revenue-maximizing virtualized network function chain placement in dynamic environment

Network Function Virtualization (NFV) is a promising paradigm which can increase network flexibility by deploying newly network services into networks. Because of the flexibility, NFV is also considered as one of the building blocks for 5G and edge computing. However, the intrinsic dynamic features of NFV and the rigorous requirements proposed by 5G and edge computing, such as delay, pose significant challenges to make the optimal Virtual Network Function (VNF) chain placement. To address this problem, we first formulate the VNF chain placement problem as an integer linear programming problem with taking the dynamic characteristics in to consideration. Then we propose an efficient dynamic algorithm, called DynAmic vnF placemenT (DAFT), which provides a good solution for VNF chain placement. DAFT is based on primal–dual technique and combines with an efficient subroutine which is solved by reducing to the shortest path problem. The theoretic analysis shows DAFT is (1−1∕e)-competitive to offline optimal solution. We also propose a modified algorithm concerning algorithm implementation issues, which is called Feasible DAFT (FDAFT). Finally, we evaluate the proposed algorithms through extensive numerical simulations. The experiment results show that DAFT and FDAFT achieve average competitive ratios up to 98.42% and 96.74%, respectively and outperform the compared algorithms around 50%.

Implementation issues in optimization algorithms: do they matter?

ABSTRACTTwo factors that have a major impact on the performance of an optimization method are (1) formal algorithm specifications and (2) practical implementations. The impact of the latter is typically ignored, although it defines the results measured in experiments. We present an in-depth study of algorithm implementation issues and ask questions such as Does optimizing the implementation of an optimization algorithm pay off? Do bugs matter? and Is using more complicated but also more efficient data structures worth the effort? The intuitive answer to all of these questions is yes, but there is little published evidence. To bridge this gap, we use one of the most studied combinatorial optimization problems – the Traveling Salesman Problem – as a test bed and implement two state-of-the-art approaches for solving it – the Lin-Kernighan Heuristic and an Ejection Chain Method. We investigate implementation effort and performance gain, in order to provide further insights to the above questions.

Exploring Multimodal Data Fusion Through Joint Decompositions with Flexible Couplings

A Bayesian framework is proposed to define flexible coupling models for joint tensor decompositions of multiple data sets. Under this framework, a natural formulation of the data fusion problem is to cast it in terms of a joint maximum a posteriori (MAP) estimator. Data driven scenarios of joint posterior distributions are provided, including general Gaussian priors and non Gaussian coupling priors. We present and discuss implementation issues of algorithms used to obtain the joint MAP estimator. We also show how this framework can be adapted to tackle the problem of joint decompositions of large datasets. In the case of a conditional Gaussian coupling with a linear transformation, we give theoretical bounds on the data fusion performance using the Bayesian Cramer-Rao bound. Simulations are reported for hybrid coupling models ranging from simple additive Gaussian models, to Gamma-type models with positive variables and to the coupling of data sets which are inherently of different size due to different resolution of the measurement devices.

Bandwidth-constrained distributed estimation for wireless sensor Networks-part I: Gaussian case

We study deterministic mean-location parameter estimation when only quantized versions of the original observations are available, due to bandwidth constraints. When the dynamic range of the parameter is small or comparable with the noise variance, we introduce a class of maximum-likelihood estimators that require transmitting just one bit per sensor to achieve an estimation variance close to that of the (clairvoyant) sample mean estimator. When the dynamic range is comparable or larger than the noise standard deviation, we show that an optimum quantization step exists to achieve the best possible variance for a given bandwidth constraint. We will also establish that in certain cases the sample mean estimator formed by quantized observations is preferable for complexity reasons. We finally touch upon algorithm implementation issues and guarantee that all the numerical maximizations required by the proposed estimators are concave.

On the numerical modelling of convex particle assemblies

A quasi-static model is proposed for the simulation of dense, randomly packed assemblies consisting of convex bodies and undergoing slow deformation. A second-order approximation of the contact conditions is first derived. The assembly equilibrium problem is formulated as a potential minimization problem subject to a set of nonlinear constraints that result from the impenetrability and sticking friction conditions. We find the solution of the nonlinear minimization problem through a sequence of approximation steps. At each step a quadratic programming subproblem is solved to compute a search direction along which a univariate nonsmooth minimization of the potential is performed. For the line search the nonlinear constraints are represented by exact penalty functions. The addition of a second-order correction step is shown to accelerate the algorithm. The paper concludes with a discussion of algorithm implementation issues and application examples.

Exploring Interior-Point Linear Programming Algorithms and Software.

Part 1 Preparations: modelling linear optimization problems the simplex algorithm a first look at an interior point algorithm. Part 2 Algorithms: the primal algorithm the dual algorithm the primal-dual algorithm implementation issues. Part 3 Solutions: the integrated environment command line operations.

On a quasi-static discrete element model of granular materials

A quasi-static discrete element model is proposed for modeling slow deformations of granular materials. A mathematical model for an assembly of convex rigid particles with deformable contacts is formulated. Particular attention is given to the special cases of rigid contacts and Coulomb friction. The assembly equilibrium problem is written as a potential minimization problem subject to a set of non-linear constraints that result from the inpenetrability and sticking friction conditions. An algorithm of the reduced gradient type is proposed that approaches the solution through a sequence of linear minimization sub-problems. The paper concludes with a discussion of algorithm implementation issues.

On the numerical modeling of convex particle assemblies with friction

A quasi-static model is proposed for the simulation of dense, randomly packed assemblies consisting of convex bodies and undergoing slow deformation. A second order approximation of the contact and sticking friction conditions is derived. The solution of the assembly equilibrium problem is approximated by a sequence of nonsmooth potential minimization problems which are transformed to smooth minimization subproblems subject to nonlinear constraints. For the treatment of the nonlinearity we introduce a second order approximation: at each step a quadratic programming subproblem is solved to compute a search direction along which a univariate nonsmooth minimization of the potential is then performed. For the line search the nonlinear constraints are expressed with the aid of exact penalty functions. The addition of a second order correction step is critical for the algorithm. The paper concludes with a discussion of algorithm implementation issues and examples that illustrate its applicability.