A pairing technique for area-efficient orthogonal drawings (extended abstract)

An orthogonal drawing of a graph is a drawing such that vertices are placed on grid points and edges are drawn as sequences of vertical and horizontal segments. In this paper we present linear time algorithms that produce orthogonal drawings of graphs with n nodes. If the maximum degree is four, then the drawing produced by our first algorithm needs area no greater than 0.76n2, and introduces no more than 2n + 2 bends. Also, every edge of such a drawing has at most two bends. Our algorithm is based on forming and placing pairs of vertices of the graph. If the maximum degree is three, then the drawing produced by our second algorithm needs at most 1/4n2 area, and at most ILn/2 + 2l + 1⌋ bends (⌊n/2⌋ + 3 bends, if the graph is biconnected), where l is the number of biconnected components that are leaves in the block tree. For biconnected graphs, this algorithm produces optimal drawings with respect to the number of bends (within a constant of two), since there is a lower bound of n/2 + 1 in the number of bends for orthogonal drawings of degree 3 graphs.