Layout graph grammars: The placement approach

Abstract

Layout graph grammars are extensions of context-free graph grammars and are introduced as a tool for syntax directed constructions of graph layouts. The constructions are based on a layout specification of the productions, which are consistently transferred to the derivations. The layout specification consists of rules for a placement of the vertices and a partial routing of the edges. It specifies minimal distances between the vertices in X- or Y-dimension. These distances can be optimized according to some formal cost measures. There is a very intuitive visual representation of the layout specifications, which stems from an elegant graphic representation of the graph grammar productions. Alternatively, the layout specifications are expressed in graph theoretic terms, and so are completely integrated into usual graph grammars. The computation of optimal layouts of graphs is a well-known NP-complete problem, even for binary trees. Therefore, we design layout graph grammars which guarantee polynomial time constructions of optimal layouts of graphs. This is achieved by the restriction to polynomial graph grammars and layout specifications, which can be computed efficiently by an attributation technique. Hence, layout graph grammars are a new and powerful tool for efficient solutions of graph layout problems. They help jumping accross the NP-completeness barrier.