Balanced Aspect Ratio Trees and Their Use for Drawing Very Large GraphsDuncan, Christian A. and Goodrich, Michael T. and Kobourov, Stephen G. (1998) Balanced Aspect Ratio Trees and Their Use for Drawing Very Large Graphs. In: Graph Drawing 6th International Symposium, GD’ 98, August 1315, 1998 , pp. 111124(Official URL: http://dx.doi.org/10.1007/3540376232_9). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540376232_9
AbstractWe describe a new approach for clusterbased drawing of very large graphs, which obtains clusters by using binary space partition (BSP) trees. We also introduce a novel BSPtype decomposition, called the balanced aspect ratio (BAR) tree, which guarantees that the cells produced are convex and have bounded aspect ratios. In addition, the tree depth is O(log n), and its construction takes O(n log n) time, where n is the number of points. We show that the BAR tree can be used to recursively divide a graph into subgraphs of roughly equal size, such that the drawing of each subgraph has a balanced aspect ratio. As a result, we obtain a representation of a graph as a collection of O(log n) layers, where each succeeding layer represents the graph in an increasing level of detail. The overall running time of the algorithm is O(n log n+m+D_0(G)), where n and m are the number of vertices and edges of the graph G, and D_0(G) is the time it takes to obtain an initial embedding of G. In particular, if the graph is planar each layer is a graph drawn with straight lines and without crossings on the n \times n grid and the running time reduces to O(n log n).
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