Computing Orthogonal Drawings in a Variable Embedding Setting

This paper addresses the classical graph drawing problem of designing an algorithm that computes an orthogonal representation with the minimum number of bends. The algorithm receives as input a 4-planar graph with a given ordering of the edges around the vertices and is allowed to change such ordering to reach the optimum. While the general problem has been shown to be NP-complete 10], polynomial time algorithms have been devised for graphs whose vertex degree is at most three 5]. We show the rst algorithm whose time complexity is exponential only in the number of vertices of degree four of the input graph. This settles a problem left as open in 6]. Our algorithm is further extended to handle graphs with vertices of degree higher than four. The analysis of the algorithm is supported by several experiments on the structure of a large set of input graphs.