Almost bend-optimal planar orthogonal drawings of biconnected degree-3 planar graphs in quadratic time

Abstract

Let G be a degree-3 planar biconnected graph with n vertices. Let Opt(G) be the minimum number of bends in any orthogonal planar drawing of G. We show that G admits a planar orthogonal drawing D with at most Opt(G)+3 bends that can constructed in O(n2) time. The fastest known algorithm for constructing a bend-minimum drawing of G has time-complexity O(n5log n) and therefore, we present a significantly faster algorithm that constructs almost bend-optimal drawings.