An algorithm for embedding a biconnected planar graph to maximize the total sum of vertex‐ and edge‐weights on the exterior window

Abstract

AbstractSuppose that a biconnected planar graph G = (V, E) is given such that each vertex and edge are weighted. This paper proposes an algorithm for finding a planar embedding such that the total sum of weights of vertices and edges on the exterior window is maximized (among all possible planar embeddings of G. Among algorithm for determining planarity of a graph there is one that uses a data structure called a PQ tree. The algorithm presented in this paper is the one which extends it and uses the PQ tree as its data structure as well. However, it can find a required planar embedding in O(|V|) time by assigning special weights to each node of each PQ tree generated in the algorithm.