A linear time heuristic for the branch-decomposition of planar graphs

Abstract

Let G be a biconnected planar graph given together with its planar drawing. Let VF(G) denote the bipartite graph on the sets of vertices and of faces of G such that each of its edges represents an incidence in G between a face and a vertex. Let αG denote the maximum distance in VF(G) from the outerface of G. We show that there always exists a branch-decomposition of G with width αG and that such a decomposition can be constructed in linear time. We also give experimental results, in which we compare the width of our decomposition with the optimal width and with the width obtained by some heuristics for general graphs proposed by previous researchers, on test instances used by those researchers. On 56 out of the total 59 test instances, our method gives a decomposition within additive 2 of the optimum width and on 33 instances it achieves the optimum width. © Springer-Verlag 2003.