Bend-Minimum Orthogonal Drawings in Quadratic Time

Let G be a planar 3-graph (i.e., a planar graph with vertex degree at most three) with n vertices. We present the first O(n(2))-time algorithm that computes a planar orthogonal drawing of G with the minimum number of bends in the variable embedding setting. If either a distinguished edge or a distinguished vertex of G is constrained to be on the external face, a bend-minimum orthogonal drawing of G that respects this constraint can be computed in O(n) time. Different from previous approaches, our algorithm does not use minimum cost flow models and computes drawings where every edge has at most two bends.