Drawing Algorithms Research Articles

A fixed-parameter algorithm for dominance drawings of DAGs

A weak dominance drawing Γ of a DAG G=(V,E) is a d-dimensional drawing such that D(u)<D(v) for every dimension D of Γ if there is a directed path from a vertex u to a vertex v in G, where D(w) is the coordinate of vertex w∈V in dimension D of Γ. If D(u)<D(v) for every dimension D of Γ, but there is no path from u to v, we have a falsely implied path (fip). Minimizing the number of fips is an important theoretical and practical problem. Computing 2-dimensional weak dominance drawings with minimum number of fips is NP-hard. We show that this problem is FPT parameterized by the dimension d and the modular width mw. A key ingredient of our proof is the Compaction Lemma, where we show an interesting property of any weak dominance drawing of G with the minimum number of fips. This FPT result in weak dominance, which is interesting by itself because the fip-minimization problem is NP-hard, is used to prove our main contributions. Computing the dominance dimension of G, that is, the minimum number of dimensions d for which G has a d-dimensional dominance drawing (a weak dominance drawing with 0 fips), is a well-known NP-hard problem. We show that the dominance dimension of G is bounded by mw2 (or mw, if mw<4) and that computing the dominance dimension of G is an FPT problem with parameter mw. As far as we know, this the first FPT-algorithm to compute the dominance dimension of a DAG.

SmartGD: A GAN-Based Graph Drawing Framework for Diverse Aesthetic Goals.

While a multitude of studies have been conducted on graph drawing, many existing methods only focus on optimizing a single aesthetic aspect of graph layouts, which can lead to sub-optimal results. There are a few existing methods that have attempted to develop a flexible solution for optimizing different aesthetic aspects measured by different aesthetic criteria. Furthermore, thanks to the significant advance in deep learning techniques, several deep learning-based layout methods were proposed recently. These methods have demonstrated the advantages of deep learning approaches for graph drawing. However, none of these existing methods can be directly applied to optimizing non-differentiable criteria without special accommodation. In this work, we propose a novel Generative Adversarial Network (GAN) based deep learning framework for graph drawing, called SmartGD, which can optimize different quantitative aesthetic goals, regardless of their differentiability. To demonstrate the effectiveness and efficiency of SmartGD, we conducted experiments on minimizing stress, minimizing edge crossing, maximizing crossing angle, maximizing shape-based metrics, and a combination of multiple aesthetics. Compared with several popular graph drawing algorithms, the experimental results show that SmartGD achieves good performance both quantitatively and qualitatively.

Virtual Drawing using OpenCV

Virtual Drawing using OpenCV

Study of image reconstruction method for 2D gamma scan technique by anti-aliasing line "Xiaolin Wu" algorithm combined with simultaneous algebraic reconstruction algorithms and testing on MCNP simulation data

Gamma scanning technique is known to be an effective method for survey the condition of distillation columns in petrochemical refineries and has been widely applied. The result of the gamma scanning is a 1-dimensional graph showing the transmittance counts according to the height of the column. To illuminate the important phenomena occurring on the tray such as foaming; flooding; weeping due to valve failure on the tray needs experienced people and the interpretation results are still quite qualitative. The method of 2-D gamma scanning and reconstruction (2D Tomography), which has just appeared in the world in recent years, is considered as a potential method to help detect the above phenomena. This report presents the two-dimensional gamma scanning configuration, mathematical calculation and noise processing methods by using the combination of Xiaolin Wu’s line drawing algorithm with simultaneous algebraic reconstruction algorithm (SART) based on data from Monte Carlo simulation.

Impact of algorithmic and data structure implementation to game development

Many game developers tend to build their proprietary game engines with various algorithmic and data structure implementations. This work discusses a game made using the Pygame library that utilizes a maze generation algorithm, collision detection algorithm, and 2d shadow drawing algorithm to analyze how programming implementation could impact the game's representation, optimization, and future development. In this paper, various algorithms and data structures are compared based on their characteristic and performance, which leads to an analysis of how the game would differ from its current state if alternative implementations are used. It also addresses the issues raised by algorithms and data structures based on their interdependence relationship.

Automorphism Faithfulness Metrics for Symmetric Graph Drawings.

In this article, we present new quality metrics for symmetric graph drawing based on group theory. Roughly speaking, the new metrics are faithfulness metrics, i.e., they measure how faithfully a drawing of a graph displays the ground truth (i.e., geometric automorphisms) of the graph as symmetries. More specifically, we introduce two types of automorphism faithfulness metrics for displaying: (1) a single geometric automorphism as a symmetry (axial or rotational), and (2) a group of geometric automorphisms (cyclic or dihedral). We present algorithms to compute the automorphism faithfulness metrics in O(n logn) time. Moreover, we also present efficient algorithms to detect exact symmetries in a graph drawing. We then validate our automorphism faithfulness metrics using deformation experiments. Finally, we use the metrics to evaluate existing graph drawing algorithms to compare how faithfully they display geometric automorphisms of a graph as symmetries.

Convex grid drawings of planar graphs with constant edge-vertex resolution

In this work, we continue the study of the area required for convex straight-line grid drawings of 3-connected plane graphs, which has been intensively investigated in the last decades. Motivated by applications, such as graph editors, we additionally require the obtained drawings to have bounded edge-vertex resolution, that is, the closest distance between a vertex and any non-incident edge in the drawing is lower bounded by a constant that does not depend on the size of the graph. We present a drawing algorithm that takes as input a 3-connected plane graph with n vertices and f internal faces, and computes a convex straight-line drawing with edge-vertex resolution at least 12 on an integer grid of size (n−2+a)×(n−2+a), where a=min⁡{n−3,f}. Our result improves the previously best-known area bound of (3n−7)×(3n−7)/2 by Chrobak, Goodrich and Tamassia.

Drawing Order Diagrams Through Two-Dimension Extension

Ordinal real-world data such as concept hierarchies, ontologies, genealogies, or task dependencies in scheduling often has the property to not only contain pairwise comparable, but also incomparable elements. Order diagrams provide an important tool for understanding and thus discovering knowledge in such data. Easily readable drawings of such order diagrams are hard to come by, even for small ordered sets. Many attempts were made to transfer classical graph drawing approaches to order diagrams. Although these methods produce satisfying results for some ordered sets, they unfortunately perform poorly in general. In this work, we present the novel algorithm DimDraw to decompose an ordered set (e.g., a concept hierarchy) in linear orders and to produce a corresponding order diagram. This algorithm is based on a relation between the dimension of an ordered set and the bipartiteness of its transitive incompatibility graph. To evaluate the quality of the algorithm, a user study was conducted where generated drawings were compared with ones from state-of-the-art drawing algorithms.

B0-VPG Representation of AT-free Outerplanar Graphs

A $k$-bend path is a non-self-intersecting polyline in the plane made of at most $k+1$ axis-parallel line segments. B$_{k}$-VPG is the class of graphs which can be represented as intersection graphs of $k$-bend paths in the same plane. In this paper, we show that all AT-free outerplanar graphs are B$_{0}$-VPG, i.e., intersection graphs of horizontal and vertical line segments in the plane. Our proofs are constructive and give a polynomial time B$_{0}$-VPG drawing algorithm for the class. In fact, we show the existence of a B$_{0}$-VPG representation for a superclass of AT-free graphs namely linear outerplanar graphs which we define as the class of subgraphs of biconnected outerpaths. Outerpaths are outerplanar graphs which admit a planar drawing whose weak dual is a path. Following a long line of improvements, Gonçalves, Isenmann, and Pennarun [SODA 2018] showed that all planar graphs are B$_{1}$-VPG. Since there are planar graphs which are not B$_{0}$-VPG, characterizing B$_{0}$-VPG graphs among planar graphs becomes interesting. Chaplick et al. [WG 2012] had shown that it is NP-complete to recognize B$_{k}$-VPG graphs within B$_{k+1}$-VPG. Hence recognizing B$_{0}$-VPG graphs within B$_{1}$-VPG is NP-complete in general, but the question is open when restricted to planar graphs. There are outerplanar graphs and AT-free planar graphs which are not B$_{0}$-VPG. This piqued our interest in AT-free outerplanar graphs.

DBSCAN-based line density clustering algorithm for CAD architectural drawings

In the traditional architecture industry, architects often need to convert CAD drawings into BIM in order to express the final effect of the building more concretely and to understand whether the design of each profession is reasonable after the drawings are completed. The whole modeling process is boring and tedious, and due to human fatigue, the final result is prone to problems, which eventually leads to failure to meet expectations. In order to free architects from the tedious task of model transformation, companies have designed software for automatic model transformation using computers. The core of the software design is related to computational geometry. Line segment clustering is one of the elements of computational geometry and a frequent problem in programming. Appropriate clustering of line segments can often bring convenience to the problem. This paper combines the basic idea of the DBSCAN algorithm, improves the shortcomings of DBSCAN algorithm in dealing with line segment clustering, and proposes a density-based line clustering algorithm with shapely library as a tool. The algorithm is highly interpretable, and the method performs well and efficiently in the test of actual drawings, whether to group the line segments or to find the target line segments that meet the conditions, which provides convenience for the subsequent calculation.

Relating planar graph drawings to planar satisfiability problems

A SAT graph G(Φ) of a satisfiability instance Φ consists of a vertex for each clause and a vertex for each variable, where there exists an edge between a clause vertex and a variable vertex if and only if the variable or its negation appears in that clause. Many satisfiability problems, which are NP-hard, become polynomial-time solvable when the SAT graph is restricted to satisfy some graph properties. A rich body of research attempts to narrow down the boundary between the NP-hardness and polynomial-time solvability of various satisfiability problems. In this paper, we examine planar satisfiability problems and leverage planar graph drawing algorithms to improve our understanding of these problems. A rich body of graph drawing algorithms exists to check whether a planar graph admits a drawing that satisfies certain drawing aesthetics. We show how the existing graph drawing knowledge could be used to establish sufficient conditions for a SAT instance to always be satisfiable and give algorithms to efficiently find a satisfying truth assignment. In some cases, our algorithm can find a truth assignment by setting a small number of variables to true, which relates to the satisfiability variants that seek to minimize the number of ones.

Intelligent Element Layout Algorithm of Ceramic Design Drawing Based on Genetic Algorithm

Conventional intelligent layout algorithm of ceramic design drawing elements mainly uses density distribution method to obtain ceramic design drawing element units, which is vulnerable to the influence of pattern density, resulting in a low distribution balance of design drawing elements. Therefore, a new intelligent layout algorithm for ceramic design drawing elements needs to be designed based on a genetic algorithm. That is, combining the characteristics of ceramic design drawing elements, the intelligent parting structure of ceramic design drawing elements is constructed, and then the brilliant layout model of ceramic design drawing elements is designed using genetic algorithm. The experimental results show that the developed intelligent layout algorithm of ceramic design elements has a high distribution balance, which proves that the designed intelligent layout algorithm of ceramic design elements has good performance, reliability, and certain application value, and has made specific contributions to improving the aesthetic quality of ceramic design drawings.

Fetal head biometrics measurements using convolutional neural network and mid-point ellipse drawing algorithm

Fetal head biometrics measurements using convolutional neural network and mid-point ellipse drawing algorithm

Factual to Virtual Visualization

The purpose of this study is to explore the formation of image output in computer system from the user input information. The study seeks to answer the research question How does the image displayed on the computer screen and how appearance of image changed? The goal is to analyze transformation of real world picture to computerized output image in a very simple method by explaining all major components involved in this process in detail with diagrams. Further by using some mathematical concepts algorithms are derived and implemented to transform the images to change their shapes, sizes etc As there is a very near context between computer science and mathematics. Systems works completely based on the algorithms written to perform the particular task, algorithms are designed based on the mathematical concepts and are implemented by the programming languages in computer. Paper concentrates on the graphic capabilities and potentials of the digital computer. It presents an abstract idea of system that, how computer works internally to create and represent the simple graphical elements and images which human can see and understand. Paper presents all the components and related concepts with suitable examples from input information to graphical output produced by computer. After by getting the concept of image formation the next step is to know that how transformation of image takes place by changing original image. This paper illustrates four types of transformations with example translation, rotation, scaling, and shearing. Paper explores about display devices, different types of display methods, programming tools and finally drawing of a simple line in computer screen using a simple line drawing algorithm. Further it elaborates the concept of pixels, resolution, aspect ratio, persistency, different types of transformations etc.,

Straight-line drawings of 1-planar graphs

A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. However, there are 1-planar graphs that do not admit a straight-line 1-planar drawing. We show that every 1-planar graph has a straight-line drawing with a two-coloring of the edges such that edges of the same color do not cross. Thus 1-planar graphs have geometric thickness two. In addition, the drawing is nearly 1-planar, that is, it is 1-planar if all fan-crossed edges are removed. An edge is fan-crossed if it is crossed by edges with a common vertex if it is crossed more than twice. The drawing algorithm uses high precision arithmetic with numbers with O(nlog⁡n) digits and computes the straight-line drawing from a 1-planar drawing in linear time on a real RAM.

Automated algorithm for drawing up a milling cartogram

Background: The milling cartogram is a technical task for the driver of a road milling cutter.&#x0D; Aim: Automation the process of drawing up a milling cartogram.&#x0D; Materials and methods: The algorithm for finding the best option is based on the generalized reduced gradient method. MS Excel is used as a software package. The sources of restrictions are the requirements of regulatory documents for the quality of milling operations.&#x0D; Results: The compiled model considers the conditions for ensuring surface drainage, as well as the restrictions provided for by the building regulations. The discrepancy between the actual cutting depth and the preferred one is accepted as the objective function. The analysis of the results of the solution is carried out and a comparison of manual and automated calculations is given.&#x0D; Conclusion: The use of the algorithm described in the article makes it possible to reduce the labor costs for drawing up a cartogram by half. Similarly, the degree of deviation of the specified cutting depth from the target is reduced, which leads to a decrease in the amount of overspending of materials during further work.

Theoretical Aspects of Predicting the Results of Development of the Armed Forces’ Capabilities, Considering the Assessments of Sufficiency of the State’s Economic Capabilities Based on the Mathematical Apparatus of S-shaped Functions

"The purpose of the study is to formulate an improved algorithm for drawing up plans for the development and strengthening of the capacities of the Armed Forces of Ukraine, especially under conditions of limited resources and unforeseen circumstances. The mathematical method is a central for studying and predicting the dynamics of Armed Forces of Ukraine development, namely the calculations carried out using the apparatus of S-shaped functions. In addition, the following methods were also used: analysis, synthesis and abstraction. As a result of the study, it was proposed the models for development of the Armed Forces of Ukraine for the medium term (6 years) and long term (12 years) prospects, considering the previous experience and unforeseen circumstances. It was proposed a system of consistent planning for the Armed Forces development. The key problem in the development and planning of the Ukrainian army is the fact that the expected results do not correspond to the planned ones. It was found a direct correlation between the demands of military system and the capabilities of socio-economic system." 10.46852/0424-2513.2s.2023.3

АЛГОРИТМ ОРГАНИЗАЦИИ ПЕРЕВОЗОК НА ОСНОВЕ КРИТИЧЕСКОГО ЭЛЕМЕНТА МАТРИЦЫ КОРРЕСПОНДЕНЦИЙ

The passenger urban transport system based on unmanned automatic transport of small capacity, which is closed, i. e. functioning independently - without human participation, is considered. Data collection, analysis and organization of transportation in such system are carried out using information technologies and intelligent algorithms. The correspondence matrix serves as an information basis for drafting a transportation plan. An algorithm for drawing up a transportation plan based on the correspondence matrix is proposed, in which the critical element correlates with the condition of sufficient accumulation of requests for transportation. In addition, the algorithm provides the possibility of in-passing transportation of passengers. It is demonstrated that the proposed algorithm makes it possible to achieve a level of comfort comparable to the comfort of a taxi ride, but at the same time, the economic effect of transportation is higher than that of a taxi, due to a larger number of passengers traveling together. The considered model is aimed at increasing the mobility and flexibility of passenger transportation in conditions of high traffic flows and is distinguished by economic and environmental benefits, since the method of passenger transportation by unmanned vehicles provides high carrying capacity of urban transport systems with a high level of passenger comfort on the route.

Development of the fundamentals for organizing the transportation of local goods on the railways of the republic of Uzbekistan

Target: The article discusses the approach to variant calculations of a phased increase in line capacity, modeling of a traffic management system aimed at meeting transportation needs and finding a balance between schedules of various categories of trains in the train schedule configuration to improve the efficiency of local freight transportation. Methods: The article uses methods from the theory of operational work, development of train schedules, graph theory, methods of system and cluster analysis, mathematical statistics, economic and mathematical modeling. Results: two-level model of transport and logistics regional network; iterative algorithm for assigning reference stations; approach to calculating the optimal weight of a local train; algorithm and recommendations for drawing up daily train schedules with local cargo. Practical significance: the results will make it possible to develop rational options for the movement of trains with local cargo on schedule in conditions of increasing transit freight traffic.

Research on Drawing Algorithm for Precise Lissajous Curves of Vibrations and its indexing of Condition Monitoring/Diagnosis Technique

Research on Drawing Algorithm for Precise Lissajous Curves of Vibrations and its indexing of Condition Monitoring/Diagnosis Technique