HARP: A Dynamic Inertial Spectral Partitioner

Partitioning unstructured graphs is central to the parallel solution of computational science and engineering problems. Spectral partitioners, such recursive spectral bisection (RSB), have proven effecfive in generating high-quality partitions of realistically-sized meshes. The major problem which hindered their wide-spread use was their long execution times. This paper presents a new inertial spectral partitioner, called HARP. The main objective of the proposed approach is to quickly partition the meshes at runtime in a manner that works efficiently for real applications in the context of distributed-memory machines. The underlying principle of HARP is to find the eigenvectors of the unpartitioned vertices and then project them onto the eigerivectors of the original mesh. Results for various meshes ranging in size from 1000 to 100,000 vertices indicate that HARP can indeed partition meshes rapidly at runtime. Experimental results show that our largest mesh can be partitioned sequentially in only a few seconds on an SP2 which is several times faster than other spectral partitioners while maintaining the solution quality of the proven RSB method. A parallel WI version of HARP has also been implemented on IBM SP2 and Cray T3E. Parallel HARP, running on 64 processors SP2 and T3E, can partition a mesh containing more than 100,000 vertices into 64 subgrids in about half a second. These results indicate that graph partitioning can now be truly embedded in dynamically-changing real-world applications

On rectangular covering problems

Many applications like picture processing, data compression or pattern recognition require a covering of a set of points most often located in the (discrete) plane by rectangles due to specific cost constraints. In this paper we provide exact dynamic programming algorithms for covering point sets by regular rectangles, that have to obey certain (parameterized) boundary conditions. The concrete representative out of a class of objective functions that is studied is to minimize sum of area, circumference and number of patches used. This objective function may be motivated by requirements of numerically solving PDE's by discretization over (adaptive multi-)grids. More precisely, we propose exact deterministic algorithms for such problems based on a (set theoretic) dynamic programming approach yielding a time bound of O(n^23^n) . In a second step this bound is (asymptotically) decreased to O(n^62^n) by exploiting the underlying rectangular and lattice structures. Finally, a generalization of the problem and its solution methods is discussed for the case of arbitrary (finite) space dimension

On rectangular covering problems

Many applications like picture processing, data compression or pattern recognition require a covering of a set of points most often located in the (discrete) plane by rectangles due to specific cost constraints. In this paper we provide exact dynamic programming algorithms for covering point sets by regular rectangles, that have to obey certain (parameterized) boundary conditions. The concrete representative out of a class of objective functions that is studied is to minimize sum of area, circumference and number of patches used. This objective function may be motivated by requirements of numerically solving PDE's by discretization over (adaptive multi-)grids. More precisely, we propose exact deterministic algorithms for such problems based on a (set theoretic) dynamic programming approach yielding a time bound of O(n^23^n) . In a second step this bound is (asymptotically) decreased to O(n^62^n) by exploiting the underlying rectangular and lattice structures. Finally, a generalization of the problem and its solution methods is discussed for the case of arbitrary (finite) space dimension

Advanced Signal Processing Techniques Applied to Power Systems Control and Analysis

The work published in this book is related to the application of advanced signal processing in smart grids, including power quality, data management, stability and economic management in presence of renewable energy sources, energy storage systems, and electric vehicles. The distinct architecture of smart grids has prompted investigations into the use of advanced algorithms combined with signal processing methods to provide optimal results. The presented applications are focused on data management with cloud computing, power quality assessment, photovoltaic power plant control, and electrical vehicle charge stations, all supported by modern AI-based optimization methods

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

Review on Radio Resource Allocation Optimization in LTE/LTE-Advanced using Game Theory

Recently, there has been a growing trend toward ap-plying game theory (GT) to various engineering fields in order to solve optimization problems with different competing entities/con-tributors/players. Researches in the fourth generation (4G) wireless network field also exploited this advanced theory to overcome long term evolution (LTE) challenges such as resource allocation, which is one of the most important research topics. In fact, an efficient de-sign of resource allocation schemes is the key to higher performance. However, the standard does not specify the optimization approach to execute the radio resource management and therefore it was left open for studies. This paper presents a survey of the existing game theory based solution for 4G-LTE radio resource allocation problem and its optimization