On Heuristics for Determining the Thickness of a Graph

We present an empirical analysis of some heuristics for the graph thickness problem, i.e., decomposing a graph into the minimum number of planar subgraphs. The problem has applications in database systems, e.g., the layout of E-R diagrams. The heuristics are based on some algorithms for nding a maximal planar subgraph of a nonplanar graph. Empirical results show that a randomized heuristic is a practical tool for solving this problem. We also improve upon a previously derived upper bound for the thickness of a graph with respect to its size.