Combining spectral sequencing and parallel simulated annealing for the MinLA problem

In this paper we present and analyze new sequential and parallel heuristics to approximate the Minimum Linear Arrangement problem (MinLA). The heuristics consist in obtaining a first global solution using Spectral Sequencing and improving it locally through Simulated Annealing. In order to accelerate the annealing process, we present a special neighborhood distribution that tends to favor moves with high probability to be accepted. We show how to make use of this neighborhood to parallelize the Metropolis stage on distributed memory machines by mapping partitions of the input graph to processors and performing moves concurrently. The paper reports the results obtained with this new heuristic when applied to a set of large graphs, including graphs arising from finite elements methods and graphs arising from VLSI applications. Compared to other heuristics, the measurements obtained show that the new heuristic improves the solution quality, decreases the running time and offers an excellent speedup when ran on a commodity network made of nine personal computers.Postprint (published version

Energy-efficient communication protocol in linear wireless sensor networks

Wireless sensor networks (WSNs) have been widely recognized as a promising technology that can enhance various aspects of structure monitoring and border surveillance. Typical applications, such as sensors embedded in the outer surface of a pipeline or mounted along the supporting structure of a bridge, feature a linear sensor arrangement. Economical power use of sensor nodes is essential for long-lasting operation. In this paper, we present wireless High-Level Data Link Control (HDLC) a novel approach to energy-efficient data routing to a single control center in a linear sensor topology. Applying a standard data layer along with a time division multiple access (TDMA)-based Medium Access Control (MAC) and time synchronization technique specifically designed for the linear topology, we address the interoperability problem with guaranteed energy efficiency and data link performance in linear sensor topology.Peer Reviewe

Probability and Problems in Euclidean Combinatorial Optimization

This article summarizes the current status of several streams of research that deal with the probability theory of problems of combinatorial optimization. There is a particular emphasis on functionals of finite point sets. The most famous example of such functionals is the length associated with the Euclidean traveling salesman problem (TSP), but closely related problems include the minimal spanning tree problem, minimal matching problems and others. Progress is also surveyed on (1) the approximation and determination of constants whose existence is known by subadditive methods, (2) the central limit problems for several functionals closely related to Euclidean functionals, and (3) analogies in the asymptotic behavior between worst-case and expected-case behavior of Euclidean problems. No attempt has been made in this survey to cover the many important applications of probability to linear programming, arrangement searching or other problems that focus on lines or planes

Probing the arrangement of hyperplanes

AbstractIn this paper we investigate the combinatorial complexity of an algorithm to determine the geometry and the topology related to an arrangement of hyperplanes in multi-dimensional Euclidean space from the “probing” on the arrangement. The “probing” by a flat means the operation from which we can obtain the intersection of the flat and the arrangement. For a finite set H of hyperplanes in Ed, we obtain the worst-case number of fixed direction line probes and that of flat probes to determine a generic line of H and H itself. We also mention the bound for the computational complexity of these algorithms based on the efficient line probing algorithm which uses the dual transform to compute a generic line of H.We also consider the problem to approximate arrangements by extending the point probing model, which have connections with computational learning theory such as learning a network of threshold functions, and introduce the vertical probing model and the level probing model. It is shown that the former is closely related to the finger probing for a polyhedron and that the latter depends on the dual graph of the arrangement.The probing for an arrangement can be used to obtain the solution for a given system of algebraic equations by decomposing the μ-resultant into linear factors. It also has interesting applications in robotics such as a motion planning using an ultrasonic device that can detect the distances to obstacles along a specified direction

The sum of edge lengths in random linear arrangements

Spatial networks are networks where nodes are located in a space equipped with a metric. Typically, the space is two-dimensional and until recently and traditionally, the metric that was usually considered was the Euclidean distance. In spatial networks, the cost of a link depends on the edge length, i.e. the distance between the nodes that define the edge. Hypothesizing that there is pressure to reduce the length of the edges of a network requires a null model, e.g., a random layout of the vertices of the network. Here we investigate the properties of the distribution of the sum of edge lengths in random linear arrangement of vertices, that has many applications in different fields. A random linear arrangement consists of an ordering of the elements of the nodes of a network being all possible orderings equally likely. The distance between two vertices is one plus the number of intermediate vertices in the ordering. Compact formulae for the 1st and 2nd moments about zero as well as the variance of the sum of edge lengths are obtained for arbitrary graphs and trees. We also analyze the evolution of that variance in Erdos-Renyi graphs and its scaling in uniformly random trees. Various developments and applications for future research are suggested

Computational analysis of transport in three-dimensional heterogeneous materials: An OpenFOAM®-based simulation framework

© 2020, The Author(s). Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated approach to generate, study and upscale transport equations in random and periodic porous structures. The geometry generation is based on random algorithms or ballistic deposition. In particular, a new algorithm is proposed to generate random packings of ellipsoids with random orientation and tunable porosity and connectivity. The porous structure is then meshed using locally refined Cartesian-based or unstructured strategies. Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical theory of homogenisation for linear advection–diffusion–reaction operators. Existing simulation codes are extended with novel developments and integrated to produce a fully open-source simulation pipeline. A showcase of a few interesting three-dimensional applications of these computational approaches is then presented. Firstly, convergence properties and the transport and dispersion properties of a periodic arrangement of spheres are studied. Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials

Computational analysis of transport in three-dimensional heterogeneous materials: An OpenFOAM®-based simulation framework

Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated approach to generate, study and upscale transport equations in random and periodic porous structures. The geometry generation is based on random algorithms or ballistic deposition. In particular, a new algorithm is proposed to generate random packings of ellipsoids with random orientation and tunable porosity and connectivity. The porous structure is then meshed using locally refined Cartesian-based or unstructured strategies. Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical theory of homogenisation for linear advection–diffusion–reaction operators. Existing simulation codes are extended with novel developments and integrated to produce a fully open-source simulation pipeline. A showcase of a few interesting three-dimensional applications of these computational approaches is then presented. Firstly, convergence properties and the transport and dispersion properties of a periodic arrangement of spheres are studied. Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials