A New Minimum Cost Flow Algorithm with Applications to Graph Drawing

Let N be a single-source single-sink ow network with n nodes, m arcs, and positive arc costs. We present a pseudo-polynomial algorithm that computes a maximum ow of minimum cost for N in time O(3=4 m p log n), where is the cost of the ow. This improves upon previously known methods for networks where the minimum cost of the ow is small. We also show an application of our ow algorithm to a well-known graph drawing problem. Namely, we show how to compute a planar orthogonal drawing with the minimum number of bends for an n-vertex embedded planar graph in time O(n 7=4 p log n). This is the rst subquadratic algorithm for bend minimization. The previous best bound for this problem was O(n 2 log n) 19].