Hierarchical planarity testing algorithms

Abstract

Using hierarchical definitions, one can describe very large graphs in small space. The blow-up from the length of the hierarchical description to the size of the graph can be as large as exponential. If the efficiency of graph algorithms is measured in terms of the length of the hierarchical description rather than in terms of the graph size, algorithms that do not exploit the hierarchy become hopelessly inefficient. Whether the hierarchy can be exploited to speed up the solution of graph problems depends on the hierarchical graph model. In the literature, hierarchical graph models have been described that allow almost no exploitation of the hierarchy [ 16]. In this paper, a hierarchical graph model that permits taking advantage of the hierarchy is presented. For this model algorithms are given that test planarity of a hierarchically described graph in linear time in the length of the hierarchical description.