We describe algorithms for drawing media, systems of states, tokens and actions that have state transition graphs in the form of partial cubes. Our algorithms are based on two principles: embedding the state transition graph in a low-dimensional integer lattice and projecting the lattice onto the plane, or drawing the medium as a planar graph with centrally symmetric faces.
We consider drawings of graphs in the plane in which vertices are assigned distinct points in the plane and edges are drawn as simple curves connecting the vertices and such that the edges intersect only at their common endpoints. There is an intuitive quality measure for drawings of a graph that measures the height of a drawing $ϕ: G \rightarrow \mathbb{R}^2$ as follows. For a vertical line $\ell$ in $\mathbb{R}^2$, let the height of $\ell$ be the cardinality of the set $\ell \cap ϕ(G)$. The height of a drawing of $G$ is the maximum height over all vertical lines. In this paper, instead of ab…
We present algorithms that extend the path-based hierarchical drawing framework and give experimental results. Our algorithms run in $O(km)$ time, where $k$ is the number of paths and $m$ is the number of edges of the graph, and provide better upper bounds than the original path based framework: e.g., the height of the resulting drawings is equal to the length of the longest path of $G$, instead of $n-1$, where $n$ is the number of nodes. Additionally, we extend this framework, by bundling and drawing all the edges of the DAG in $O(m + n \log n)$ time, using minimum extra width per path. We al…
A planar orthogonal drawing of a planar 4-graph G (i.e., a planar graph with vertex-degree at most four) is a crossing-free drawing that maps each vertex of G to a distinct point of the plane and each edge of $G$ to a sequence of horizontal and vertical segments between its end-points. A longstanding open question in Graph Drawing, dating back over 30 years, is whether there exists a linear-time algorithm to compute an orthogonal drawing of a plane 4-graph with the minimum number of bends. The term "plane" indicates that the input graph comes together with a planar embedding, which must be pre…
Shape-based metrics measure how faithfully a drawing D represents the structure of a graph G, using the proximity graph S of D. While some limited graph classes admit proximity drawings (i.e., optimally shape-faithful drawings, where S = G), algorithms for shape-faithful drawings of general graphs have not been investigated. In this paper, we present the first study for shape-faithful drawings of general graphs. First, we conduct extensive comparison experiments for popular graph layouts using the shape-based metrics, and examine the properties of highly shape-faithful drawings. Then, we prese…
Streamed Graph Drawing and the File Maintenance Problem
在流式图形绘制中，平面图G作为数据流递增地给出，并且在每个新的边被释放之后必须更新G的直线图。为了保持心理地图，每次更新后，对绘图的更改应最小化，Binucci et al.show认为，如果不允许边缘移动，指数区域对于树的一些流图绘图是必要的和足够的。我们表明，一些流图图纸可以，事实上，多项式区域，包括平面流图图纸的树，树地图，和outerplanar图，如果我们允许少量的坐标移动后，每次更新。我们的算法涉及一个有趣的连接到一个经典的算法问题-文件维护问题-我们也给这个问题的新算法在一个框架中，允许大容量内存移动。
We show how to test in linear time whether an outerplanar graph admits a planar rectilinear drawing, both if the graph has a prescribed plane embedding that the drawing has to respect and if it does not. Our algorithm returns a planar rectilinear drawing if the graph admits one.
同一图形的两个直线平面图之间的变形是从第一个图到第二个图的连续变换，使得平面性始终保持不变。变形的每一步都沿直线以恒定速度移动每个顶点。尽管在几十年前就已经确定了任何两个图形之间存在变形，但直到最近才证明多项式数量的步骤足以使任何两个平面直线图形变形。也就是说，在SODA 2013年，Alamdari et al. [1]证明了平面图的任意两个平面直线图都可以在O（n^4）步内变形，而如果我们限制为极大平面图，则O（n^2）步就足够了。本文改进了这一结果，给出了一个O（n^2）步变形平面图的任意两个平面直线图的算法，并进一步证明了串-并联图的任意两个平面直线图之间存在一个O（n）步变形.
We continue the study of the area requirement of 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 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 str…
In this paper, we present new quality metrics for dynamic graph drawings. Namely, we present a new framework for change faithfulness metrics for dynamic graph drawings, which compare the ground truth change in dynamic graphs and the geometric change in drawings. More specifically, we present two specific instances, cluster change faithfulness metrics and distance change faithfulness metrics. We first validate the effectiveness of our new metrics using deformation experiments. Then we compare various graph drawing algorithms using our metrics. Our experiments confirm that the best cluster (resp…
In an upward-planar L-drawing of a directed acyclic graph (DAG) each edge $e$ is represented as a polyline composed of a vertical segment with its lowest endpoint at the tail of $e$ and of a horizontal segment ending at the head of $e$. Distinct edges may overlap, but not cross. Recently, upward-planar L-drawings have been studied for $st$-graphs, i.e., planar DAGs with a single source $s$ and a single sink $t$ containing an edge directed from $s$ to $t$. It is known that a plane $st$-graph, i.e., an embedded $st$-graph in which the edge $(s,t)$ is incident to the outer face, admits an upward-…
We study the algorithmic problem of computing drawings of graphs in which $(i)$ each vertex is a disk with fixed radius $ρ$, $(ii)$ each edge is a straight-line segment connecting the centers of the two disks representing its end-vertices, $(iii)$ no two disks intersect, and $(iv)$ the distance between an edge segment and the center of a non-incident disk, called \emph{edge-vertex resolution}, is at least $ρ$. We call such drawings \emph{disk-link drawings}. In this paper we focus on the case of constant edge-vertex resolution, namely $ρ=\frac{1}{2}$ (i.e., disks of unit diameter). We prove th…
