Drawing clustered graphs on an orthogonal grid

Abstract

Abstract. 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 algorithm which produces such drawings with O(n 2) area and with 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 in each edge. IntroductionClustered graphs are graphs with recursive clustering structures over the vertices (see Figure 1). Algorithms for constructing straight-line drawings of clustered graphs are given in [8,11]; note, however, that straight-line drawings of clustered graphs can require exponential area [11]. In this paper, we present an algorithm which produce planar drawings of clustered graphs in a convention called "orthogonM grid rectangular cluster drawings". We apply a technique to order the clusters of the graph recursively, and we use the visibility representation for directed graphs to produce our drawings. The orthogonM grid drawing convention appears in a number of applications, such as VLSI circuit design [20,21,37,38] and diagrammatic interfaces for relational information systems [1,2,24,27,31]. Under the orthogonal grid drawing convention, minimizing the number of bends and minimizing the area are the