planar-graph | 易学教程

small cycle finding in a planar graph

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问题 I have a geometric undirected planar graph, that is a graph where each node has a location and no 2 edges cross, and I want to find all cycles that have no edges crossing them. Are there any good solutions known to this problem? What I'm planning on doing is a sort of A* like solution: insert every edge in a min heap as a path extend the shortest path with every option cull paths that loop back to other than there start (might not be needed) cull paths that would be the third to use ang given

Algorithm for the Planarization of a non-planar Graph

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问题 Is there a popular algorithm for the planarization of a non-planar graph. I'm currently planning to implement a Orthogonal Planar Layout algorithm for undirected graphs in Boost ( Boost Graph Library ). BGL has an implementation to check the planarity of an undirected graph ( Boyer-Myrvold Planarity Testing ) and I plan to use the planar embedding returned by this method to do an orthogonal layout. But I'm not sure what should be done if the input graph is non-planar. Should I do something

Minimizing number of crossings in a bipartite graph

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问题 The following algorithm problem occurred to me while drawing a graph for something unrelated: We have a plane drawing of a bipartite graph, with the disjoint sets arranged in columns as shown. How can we rearrange the nodes within each column so that the number of edge crossings is minimized? I know this problem is NP-hard for general graphs (link), but is there some trick considering that the graph is bipartite? As a follow-up, what if there is a third column w , which only has edges to v ?

How to check if a Graph is a Planar Graph or not?

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问题 I'm learning about the Planar Graph and coloring in c++. But i don't know install the algorithm to do this work. Someone please help me? Here i have some information for you! This is my code! And it still has a function does not finish. If someone know what is a "Planar Graph", please fix the Planar_Graph function below! :D thanks so much! :x # define MAX 100 int kt[MAX]; int tk=0; int my_array[MAX][MAX]; // Graph FILE *f; int n,m; //m: Edge, n: Vertex int index[MAX]; int ke[MAX]; int Color

Connect an even number of nodes without intersection

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问题 I have two sets of n nodes. Now I want to connect each node from one set with another node from the other set. The resulting graph should have no intersections. I know of several sweep line algorithms (Bentley-Ottmann-Algorithm to check where intersections occur, but I couldn't find an algorithm to solve those intersections, except for a brute-force approach. Each node from one set can be connected to any other node within the other set. Any pointers to (an efficient) algorithm that solves

Connect an even number of nodes without intersection

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I have two sets of n nodes. Now I want to connect each node from one set with another node from the other set. The resulting graph should have no intersections. I know of several sweep line algorithms ( Bentley-Ottmann-Algorithm to check where intersections occur, but I couldn't find an algorithm to solve those intersections, except for a brute-force approach. Each node from one set can be connected to any other node within the other set. Any pointers to (an efficient) algorithm that solves this problem? No implementation needed. EDIT1 : Here is one solution to the problem for n=7 : The black

Algorithm for the Planarization of a non-planar Graph

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Is there a popular algorithm for the planarization of a non-planar graph. I'm currently planning to implement a Orthogonal Planar Layout algorithm for undirected graphs in Boost ( Boost Graph Library ). BGL has an implementation to check the planarity of an undirected graph ( Boyer-Myrvold Planarity Testing ) and I plan to use the planar embedding returned by this method to do an orthogonal layout. But I'm not sure what should be done if the input graph is non-planar. Should I do something with the Kuratowski sub-graph returned in such a scenario to make the graph planar. A Google Search on

Minimizing number of crossings in a bipartite graph

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The following algorithm problem occurred to me while drawing a graph for something unrelated: We have a plane drawing of a bipartite graph, with the disjoint sets arranged in columns as shown. How can we rearrange the nodes within each column so that the number of edge crossings is minimized? I know this problem is NP-hard for general graphs ( link ), but is there some trick considering that the graph is bipartite? As a follow-up, what if there is a third column w , which only has edges to v ? Or further? The paper On the one-sided crossing minimization in a bipartite graph with large degrees

Generate a large random planar graph

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What is the most efficient way to generate a large (~ 300k vertices) random planar graph ("random" here means uniformly distributed)? Another possibility consists in randomly choosing coordinates and then compute a Delaunay Triangulation, which is a planar graph (and looks nice as well). See http://en.wikipedia.org/wiki/Delaunay_triangulation There are O(n log(n)) algorithms to compute such a triangulation. Without any other requirements, I'd say look up random maze generation. If you want cycles in the graph, remove some walls at random from a simple maze. The intersections in the maze become

Generate a large random planar graph

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问题 What is the most efficient way to generate a large (~ 300k vertices) random planar graph ("random" here means uniformly distributed)? 回答1: Another possibility consists in randomly choosing coordinates and then compute a Delaunay Triangulation, which is a planar graph (and looks nice as well). See http://en.wikipedia.org/wiki/Delaunay_triangulation There are O(n log(n)) algorithms to compute such a triangulation. 回答2: Have you looked at Boltzmann sampling? See the paper by Eric Fusy "Uniform