scholarly journals Improvements to a Peak Assignment Algorithm for Two-Dimensional NMR Correlation Spectra of Zeolites Using Graph Theory

2004 ◽  
Vol 3 (3) ◽  
pp. 103-108 ◽  
Author(s):  
Darren H. BROUWER ◽  
E. Keith LLOYD
Keyword(s):  
Graph Theory ◽  
Two Dimensional ◽  
Assignment Algorithm ◽  
Peak Assignment

scholarly journals A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

2021 ◽  
Author(s):  
Leandro Pinto Fava ◽  
João Carlos Furtado ◽  
Gilson Augusto Helfer ◽  
Marko Beko ◽  
Sérgio Duarte Correia ◽  
...  
Keyword(s):  
Graph Theory ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Neighborhood Search ◽  
Two Dimensional ◽  
Routing Problem ◽  
Capacitated Vehicle Routing Problem ◽  
Graph Modeling ◽  
Loading Constraints ◽  
Capacitated Vehicle

This work presents a multi-start algorithm for solving the capacitated vehicle routing problem with two-dimensional loading constraints (2L-CVRP) allowing for the rotation of goods. Researches dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics such as the Constructive Genetic Algorithm (CGA), to construct promising initial solutions; a Tabu Search (TS), to improve the initial solutions on the routing problem; and a Large Neighborhood Search (LNS), for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multi-threading programming to improve the performance. Additionally, memory structures, like hash-tables, were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest of the community involved in symmetry studies, such as, graph algorithms and graph theory.

scholarly journals Balanced Centrality of Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Mark Debono ◽  
Josef Lauri ◽  
Irene Sciriha
Keyword(s):  
Graph Theory ◽  
Network Analysis ◽  
Linear Combination ◽  
Linear Algebra ◽  
Adjacency Matrix ◽  
Clear Understanding ◽  
Degree Centrality ◽  
Two Dimensional ◽  
Dimensional Array

There is an age-old question in all branches of network analysis. What makes an actor in a network important, courted, or sought? Both Crossley and Bonacich contend that rather than its intrinsic wealth or value, an actor’s status lies in the structures of its interactions with other actors. Since pairwise relation data in a network can be stored in a two-dimensional array or matrix, graph theory and linear algebra lend themselves as great tools to gauge the centrality (interpreted as importance, power, or popularity, depending on the purpose of the network) of each actor. We express known and new centralities in terms of only two matrices associated with the network. We show that derivations of these expressions can be handled exclusively through the main eigenvectors (not orthogonal to the all-one vector) associated with the adjacency matrix. We also propose a centrality vector (SWIPD) which is a linear combination of the square, walk, power, and degree centrality vectors with weightings of the various centralities depending on the purpose of the network. By comparing actors’ scores for various weightings, a clear understanding of which actors are most central is obtained. Moreover, for threshold networks, the (SWIPD) measure turns out to be independent of the weightings.

scholarly journals DIMENSION REDUCTION USING THE INVERSE STAMPING METHOD

2021 ◽  
Vol 2021 (4) ◽  
pp. 4810-4817
Author(s):  
JAROMIR KASPAR ◽  
◽  
MARCEL SVAGR ◽  
PETR BERNARDIN ◽  
VACLAVA LASOVA ◽  
...  
Keyword(s):  
Graph Theory ◽  
Dimension Reduction ◽  
Automotive Industry ◽  
Three Dimensional ◽  
Stochastic Methods ◽  
Complex Structures ◽  
Two Dimensional ◽  
Crucial Step ◽  
Development Tool ◽  
Wide Range

The aim of this work is to improve the inverse stamping method and increase its robustness. The first, crucial step of inverse stamping is the reduction of the three-dimensional part into a two-dimensional flat plane. There are several methods for reducing the dimension. These are geometrical methods, methods based on graph theory and stochastic methods. We examine the last two methods because of their reliability. These methods can even be used for geometrically complex structures which include holes, hooks and walls perpendicular to the flat plane. An algorithm which combines several methods for dimension reduction is proposed for use for a wide range of parts. Deep drawing is a widely used technology in the automotive industry and inverse stamping is a useful development tool.

A Manipulation of Two-Dimensional NMR Spectra Based on Graph Theory

1993 ◽  
Vol 102 (1) ◽  
pp. 24-28 ◽  
Author(s):  
A.H. Lipkus ◽  
R.A. Nieman ◽  
M.E. Munk
Keyword(s):  
Graph Theory ◽  
Nmr Spectra ◽  
Two Dimensional

scholarly journals Joint Polarization and Frequency Assignment Algorithm Based on Graph Theory

2016 ◽  
Vol 41 (8) ◽  
pp. 954-957
Author(s):  
Bonhong Koo ◽  
Chan-Byoung Chae ◽  
Sung-Ho Park ◽  
Hwi-Sung Park ◽  
Jae-Hyun Ham
Keyword(s):  
Graph Theory ◽  
Frequency Assignment ◽  
Assignment Algorithm
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