问题描述
以树的形式布置 DAG 中的顶点(即顶部没有入边的顶点，顶点仅依赖于下一层的顶点等)相当简单，无需图形绘制算法，例如 Efficient Sugiyama.但是，是否有一种简单的算法可以最大限度地减少边缘交叉?(对于某些图形，可能无法完全消除边缘交叉.)一张图说了一千个字，那么是否有一种算法可以建议 没有交叉边缘的东西.(noparr7c7A"">noparrn reln 结果
我接受了 Senthil 的建议使用 graphviz/dot -- 快速浏览一下文档可以确认 将其用作库或外部工具，以及 输出格式非常容易解析.但是，我最终选择使用 GraphSharp 代替，因为我已经在使用 .NET 等(尽管它是绝对没有点那么强大).结果是足够好"，并且可以通过一些边缘路由和调整来做得更好(模糊的文本是因为 3.5 WPF).
这是完整的 C# 代码(这是所有引用 QuickGraph 或 GraphSharp 的代码——是的；就是这么简单):
内部静态类LayoutManager{private const string ALGORITHM_NAME = "EfficientSugiyama";private const bool MINIMIZE_EDGE_LENGTH = true;私人常量双VERTEX_DISTANCE = 25;私有常量双 LAYER_DISTANCE = 25;私有常量双 MIN_CANVAS_OFFSET = 20;public static void doLayout(GraphCanvas canvas){//TODO 使用后台线程//TODO 添加注释canvas.IsEnabled = false;canvas.Cursor = Cursors.Wait;var graph = new BidirectionalGraph();var position = new Dictionary();var size = new Dictionary();foreach(canvas.nodes 中的 var 节点){var size = node.RenderSize;graph.AddVertex(节点)；position.Add(node, new Point(node.left + size.Width/2, node.top + size.Height/2));大小.添加(节点，大小)；}foreach(canvas.edges 中的 var 边){graph.AddEdge(new LayoutEdge(edge));}var context = new LayoutContext>(图形，位置，大小，LayoutMode.Simple)；var parameters = new EfficientSugiyamaLayoutParameters();parameters.VertexDistance = VERTEX_DISTANCE;parameters.MinimizeEdgeLength = MINIMIZE_EDGE_LENGTH;parameters.LayerDistance = LAYER_DISTANCE;var factory = new StandardLayoutAlgorithmFactory>();var algorithm = factory.CreateAlgorithm(ALGORITHM_NAME, context, parameters);算法.Compute();canvas.deselectAll();var minx = algorithm.VertexPositions.Select(kvp => kvp.Value.X - (kvp.Key.RenderSize.Width/2)).Aggregate(Math.Min);var miny = algorithm.VertexPositions.Select(kvp => kvp.Value.Y - (kvp.Key.RenderSize.Height/2)).Aggregate(Math.Min);minx -= MIN_CANVAS_OFFSET;最小 -= MIN_CANVAS_OFFSET;minx = minx {私有只读 ConnectingEdge _edge；公共 LayoutEdge(ConnectingEdge 边缘){ _edge = 边缘；}public GraphNode Source { get { return _edge.output.node;} }公共 GraphNode 目标 { 获取 { 返回 _edge.input.node;} }}Dot 看起来很合适:
dot - 分层"或分层有向图的绘制.这布局算法的目标是边缘相同的方向(从上到下，或左向右)，然后试图避免边缘交叉并减少边缘长度.
https://docs.google.com/viewer?url=http://www.graphviz.org/pdf/dotguide.pdf
Laying out the verticies in a DAG in a tree form (i.e. verticies with no in-edges on top, verticies dependent only on those on the next level, etc.) is rather simple without graph drawing algorithms such as Efficient Sugiyama. However, is there a simple algorithm to do this that minimizes edge crossing? (For some graphs, it may be impossible to completely eliminate edge crossing.) A picture says a thousand words, so is there an algorithm that would suggest something without crossing edges. (compared to this).
EDIT: The result
I've accepted Senthil's suggesting graphviz/dot -- a quick look at the docs confirms that it's very easy to use it as a library or external tool, and the output format is surprisingly easy to parse. However, I ended up choosing to use GraphSharp instead since I'm already using .NET, etc (though it's definitely not as powerful as dot). The result is "good enough", and could be made a lot better with a little edge routing and tweaking (the blurry text is because of 3.5 WPF).
Here's the complete C# code (this is all the code that references either QuickGraph or GraphSharp -- yeah; it was that easy):
internal static class LayoutManager
{
private const string ALGORITHM_NAME = "EfficientSugiyama";
private const bool MINIMIZE_EDGE_LENGTH = true;
private const double VERTEX_DISTANCE = 25;
private const double LAYER_DISTANCE = 25;
private const double MIN_CANVAS_OFFSET = 20;
public static void doLayout(GraphCanvas canvas)
{
// TODO use a background thread
// TODO add comments
canvas.IsEnabled = false;
canvas.Cursor = Cursors.Wait;
var graph = new BidirectionalGraph<GraphNode, LayoutEdge>();
var positions = new Dictionary<GraphNode, Point>();
var sizes = new Dictionary<GraphNode, Size>();
foreach(var node in canvas.nodes)
{
var size = node.RenderSize;
graph.AddVertex(node);
positions.Add(node, new Point(node.left + size.Width / 2, node.top + size.Height / 2));
sizes.Add(node, size);
}
foreach(var edge in canvas.edges)
{
graph.AddEdge(new LayoutEdge(edge));
}
var context = new LayoutContext<GraphNode, LayoutEdge, BidirectionalGraph<GraphNode, LayoutEdge>>(graph, positions, sizes, LayoutMode.Simple);
var parameters = new EfficientSugiyamaLayoutParameters();
parameters.VertexDistance = VERTEX_DISTANCE;
parameters.MinimizeEdgeLength = MINIMIZE_EDGE_LENGTH;
parameters.LayerDistance = LAYER_DISTANCE;
var factory = new StandardLayoutAlgorithmFactory<GraphNode, LayoutEdge, BidirectionalGraph<GraphNode, LayoutEdge>>();
var algorithm = factory.CreateAlgorithm(ALGORITHM_NAME, context, parameters);
algorithm.Compute();
canvas.deselectAll();
var minx = algorithm.VertexPositions.Select(kvp => kvp.Value.X - (kvp.Key.RenderSize.Width / 2)).Aggregate(Math.Min);
var miny = algorithm.VertexPositions.Select(kvp => kvp.Value.Y - (kvp.Key.RenderSize.Height / 2)).Aggregate(Math.Min);
minx -= MIN_CANVAS_OFFSET;
miny -= MIN_CANVAS_OFFSET;
minx = minx < 0 ? -minx : 0;
miny = miny < 0 ? -miny : 0;
foreach(var kvp in algorithm.VertexPositions)
{
var node = kvp.Key;
var pos = kvp.Value;
node.left = (pos.X - (node.RenderSize.Width / 2)) + minx;
node.top = (pos.Y - (node.RenderSize.Height / 2)) + miny;
}
canvas.Cursor = Cursors.Arrow;
canvas.IsEnabled = true;
}
private sealed class LayoutEdge : IEdge<GraphNode>
{
private readonly ConnectingEdge _edge;
public LayoutEdge(ConnectingEdge edge) { _edge = edge; }
public GraphNode Source { get { return _edge.output.node; } }
public GraphNode Target { get { return _edge.input.node; } }
}
Dot seems like it would fit the bill:
https://docs.google.com/viewer?url=http://www.graphviz.org/pdf/dotguide.pdf
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