Force-directed Graph Drawing Algorithms Research Articles

Application of a Force-Directed Graph Drawing Algorithm for the Analysis of Curricula of Educational Programs of Higher Education

Работа посвящена разработке подхода к анализу учебных планов образовательных программ высшего образования в условиях действующих федеральных государственных образовательных стандартов с точки зрения достижения заявленных образовательных результатов в виде набора компетенций. Данный подход может оказаться полезным для создания автоматизированных средств оценки качества и сравнительного анализа образовательных программ. На основе компетентностного подхода предложена модель представления учебного плана в виде простого взвешенного неориентированного графа. Предложен подход к визуализации графовового представления учебного плана на основе применения силового алгоритма визуализации, обеспечивающего достижение максимальной наглядности. Предложен подход к определению междисциплинарных связей образовательных единиц учебного плана через на основе их трудоемкости и формируемым компетенциям. Полученное визуальное представление междисциплинарных связей помогает лучше понять структуру учебного плана, выявить дисциплины с максимальным числом междисциплинарных связей, а также произвести декомпозицию плана на кластеры наиболее связанных между собой дисциплин. Предложены варианты интегральных характеристик графовых представлений учебных планов, на основе которых можно проводить их оценку, а также сравнительный анализ соответствующих образовательных программ. В качестве примеров рассмотрены учебные планы подготовки бакалавров по направлениям 09.03.01 «Информатика и вычислительная техника» и 09.03.03 «Прикладная информатика», реализуемых в институте космических и информационных технологий ФГАОУ ВО «Сибирский федеральный университет». The work is devoted to the development of an approach to the analysis of curricula of educational programs of higher education in the context of the current federal state educational standards in terms of achieving the declared learning outcomes formulated in the form of a set of competencies. This approach may prove useful for developing automated tools for assessing the quality of educational programs, as well as their comparative analysis.We propose a model for representing the curriculum in the form of a simple weighted undirected graph based on the competence-based approach. We propose an approach to the visualization of the graph representation of the curriculum based on the use of a force-directed graph drawing algorithm, which ensures achieving maximum visibility. We propose an approach to determine the interdisciplinary links of educational units of the curriculum based on their total number of credits and the competencies they are involved in. The resulting visual representation of interdisciplinary connections helps to better understand the structure of the curriculum, identify disciplines with the maximum number of interdisciplinary connections, and also decompose the plan into clusters of the most interconnected disciplines. We propose options for defining integral characteristics of graph representations of curricula, based on which the curricula can be evaluated, as well as a comparative analysis of the corresponding educational programs can be performed. As examples, we consider the curricula for the of bachelor programs majoring in 09.03.01 "Computer Science and Computer Engineering" and 09.03.03 "Applied Computer Science ", implemented at the Institute of Space and Information Technology of Siberian Federal University.

A coarsening method for bipartite networks via weight-constrained label propagation

A multilevel method is a scalable strategy to solve optimization problems in large bipartite networks, which operates in three stages. Initially the input network is iteratively coarsened into a hierarchy of gradually smaller networks. Coarsening implies in collapsing vertices into so-called super-vertices which inherit properties of their originating vertices. An initial solution is obtained executing the target algorithm in the coarsest network. Finally, this solution is successively projected back over the inverse sequence of coarsened networks, up to the initial one, yielding an approximate final solution. Despite its potential applicability, the strategy faces several theoretical and practical limitations. Coarsening is usually attained following a user-defined policy to match vertices pairwise. However, the network reduction process is extremely slow and may yield degraded solutions due to propagation of poor matches. Additionally, proper parameterization of coarsening algorithms is difficult, as well as ensuring the super-vertices preserve the relevant properties. We address these issues with a near-linear complexity coarsening strategy based on weight-constrained label propagation. Our strategy collapses groups of vertices, rather than pairs, yielding faster and more extensive network reduction. Moreover, users may specify the desired size of the coarsest network and control super-vertex weights. The applicability of our solution is illustrated in multiple scenarios, namely: multilevel implementation of an existing high-cost community detection algorithm; as a direct community detection algorithm; finally, network visualization, in connection with force-directed graph drawing algorithms. Results provide empirical evidence on the potential of our proposal to foster novel applications of the multilevel method in bipartite networks.

EClerize: A customized force-directed graph drawing algorithm for biological graphs with EC attributes.

Visualizing large-scale data produced by the high throughput experiments as a biological graph leads to better understanding and analysis. This study describes a customized force-directed layout algorithm, EClerize, for biological graphs that represent pathways in which the nodes are associated with Enzyme Commission (EC) attributes. The nodes with the same EC class numbers are treated as members of the same cluster. Positions of nodes are then determined based on both the biological similarity and the connection structure. EClerize minimizes the intra-cluster distance, that is the distance between the nodes of the same EC cluster and maximizes the inter-cluster distance, that is the distance between two distinct EC clusters. EClerize is tested on a number of biological pathways and the improvement brought in is presented with respect to the original algorithm. EClerize is available as a plug-in to Cytoscape ( http://apps.cytoscape.org/apps/eclerize ).

INTERACTIVE LAND-USE OPTIMIZATION USING LAGUERRE VORONOI DIAGRAM WITH DYNAMIC GENERATING POINT ALLOCATION

Abstract. In this work, we devise an efficient method for the land-use optimization problem based on Laguerre Voronoi diagram. Previous Voronoi diagram-based methods are more efficient and more suitable for interactive design than discrete optimization-based method, but, in many cases, their outputs do not satisfy area constraints. To cope with the problem, we propose a force-directed graph drawing algorithm, which automatically allocates generating points of Voronoi diagram to appropriate positions. Then, we construct a Laguerre Voronoi diagram based on these generating points, use linear programs to adjust each cell, and reconstruct the diagram based on the adjustment. We adopt the proposed method to the practical case study of Chiang Mai University’s allocated land for a mixed-use complex. For this case study, compared to other Voronoi diagram-based method, we decrease the land allocation error by 62.557 %. Although our computation time is larger than the previous Voronoi-diagram-based method, it is still suitable for interactive design.

Optimization of a furniture factory layout

This paper deals with the problem of optimizing a factory floor layout in a Slovenian furniture factory. First, the current state of the manufacturing system is analyzed by constructing a discrete event simulation (DES) model that reflects the manufacturing processes. The company produces over 10,000 different products, and their manufacturing processes include approximately 30,000 subprocesses. Therefore, manually constructing a model to include every subprocess is not feasible. To overcome this problem, a method for automated model construction was developed to construct a DES model based on a selection of manufacturing orders and relevant subprocesses. The obtained simulation model provided insight into the manufacturing processes and enable easy modification of model parameters for optimizing the manufacturing processes. Finally, the optimization problem was solved: the total distance the products had to traverse between machines was minimized by devising an optimal machine layout. With the introduction of certain simplifications, the problem was best described as a quadratic assignment problem. A novel heuristic method based on force-directed graph drawing algorithms was developed. Optimizing the floor layout resulted in a significant reduction of total travel distance for the products.

Research of Automatic Drawing Scheduling Network Method Based on Force-Directed

Automatic drawing algorithm has been one of the hotspot in research of drawing. So far there is no completely effective method. Force-directed graph drawing algorithm is based on physics model, makes the drawing problem into force for solving the problem in physics, then into unconstrained optimization for solving the problem in mathematics. Its advantage is based on people familiar with the physical model, and the principle is easy to understand. We can draw large-scale graphics with symmetrical and beautiful appearance through certain set and the improvement. At the advantages of Force-directed algorithm, this paper presents force-directed algorithm can be applied to automatic drawing in scheduling network, and explores the image style in a more intuitive graphical way to show the connection between scheduling network vertices.

Techniques for Edge Stratification of Complex Graph Drawings

We propose an approach that allows a user (e.g., an analyst) to explore a layout produced by any graph drawing algorithm, in order to reduce the visual complexity and clarify its presentation. Our approach is based on stratifying the drawing into layers with desired properties; to this aim, heuristics are presented. The produced layers can be explored and combined by the user to gradually acquire details. We present a user study to test the effectiveness of our approach. Furthermore, we performed an experimental analysis on popular force-directed graph drawing algorithms, in order to evaluate what is the algorithm that produces the smallest number of layers and if there is any correlation between the number of crossings and the number of layers of a graph layout. The proposed approach is useful to explore graph layouts, as confirmed by the presented user study. Furthermore, interesting considerations arise from the experimental evaluation, in particular, our results suggest that the number of layers of a graph layout may represent a reliable measure of its visual complexity. The algorithms presented in this paper can be effectively applied to graph layouts with a few hundreds of edges and vertices. For larger drawings that contain lots of crossings, the time complexity of our algorithms grows quadratically in the number of edges and more efficient techniques need to be devised. The proposed approach takes as input a layout produced by any graph drawing algorithm, therefore it can be applied in a variety of application domains. Several research directions can be explored to extend our framework and to devise new visualization paradigms to effectively present stratified drawings.