Balanced Aspect Ratio Trees and Their Use for Drawing Large Graphs
Christian A. Duncan, Michael T. Goodrich, Stephen Kobourov · Journal of Graph Algorithms and Applications · 2000
We describe a new approach for cluster-based drawing of large graphs, which obtains clusters by using binary space partition (BSP) trees. We also introduce a novel BSP-type 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 embedded in the plane 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+D0 (G)), where n and m are the number of vertices and edges of the graph G, and D0 (G) is the time it takes to obtain an initial ...