Drawing Clustered Graphs on an Orthogonal Grid
نویسندگان
چکیده
Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which produces planar drawings of clustered graphs in a convention known as orthogonal grid rectangular cluster drawings. We present an O(n) time algorithm which produces such drawings. If the input graph has n vertices then the output drawing has O(n 2 ) area and at most 3 bends in each edge. This result is as good as existing results for classical planar graphs. Further, we show that our algorithm is optimal in terms of the number of bends per edge.
منابع مشابه
Two-Bend Three-Dimensional Orthogonal Grid Drawing of Maximum Degree Five Graphs
Some recent algorithms for 3-dimensional orthogonal graph drawing use no more than 3 bends per edge route. It is unknown if there exists a graph requiring a 3-bend edge route. In this paper we present an algorithm for 2-bend 3-dimensional orthogonal grid drawing of maximum degree 5 graphs. In addition 2-bend 3-dimensional grid drawings of the 6-regular multi-partite graphs are given.
متن کاملA Better Heuristic for Orthogonal Graph Drawings
16 We end this paper by mentioning some open problems and directions for further research: Valiant proved that a grid-area of (n 2) is necessary for drawing non-planar graphs, since the crossing number can be (n 2) 26]. However, the involved constants are very small. For planar graphs (crossing number 0) a drawing with grid-area O(n log 2 n) is possible 14, 26], and the best known lower bound i...
متن کاملTwo Algorithms for Three Dimensional Orthogonal Graph Drawing
We use basic results from graph theory to design two algorithms for constructing 3-dimensional, intersection-free orthogonal grid drawings of n vertex graphs of maximum degree 6. Our first algorithm gives drawings bounded by an O(x/~ ) • O(x/~ • O(v~ ) box; each edge route contains at most 7 bends. The best previous result generated edge routes containing up to 16 bends per route. Our second al...
متن کاملOptimal three-dimensional orthogonal graph drawing in the general position model
Let G be a graph with maximum degree at most six. A three-dimensional orthogonal drawing of G positions the vertices at grid-points in the three-dimensional orthogonal grid, and routes edges along grid lines such that edge routes only intersect at common end-vertices. In this paper, we consider three-dimensional orthogonal drawings in the general position model; here no two vertices are in a co...
متن کاملAlgorithms for Drawing Plane Graphs
Graph drawing addresses the problem of constructing geometric representation of information and finds applications in almost every branch of science and technology. Efficient algorithms are essential for automatic drawings of graphs, and hence a lot of research has been carried out in the last decade by many researchers over the world to develop efficient algorithms for drawing graphs. In this ...
متن کامل