Network-Design Problems in Graphs and on the Plane

Given points in the plane, connect them using minimum ink.
Though the task seems simple, it turns out to be very time consuming. In fact, scientists believe that computers cannot efficiently solve it. So, do we have to resign?

This book examines such NP-hard network-design problems, from connectivity problems in graphs to polygonal drawing problems on the plane. First, we observe why it is so hard to optimally solve these problems. Then, we go over to attack them anyway. We develop fast algorithms that find approximate solutions that are very close to the optimal ones. Hence, connecting points with slightly more ink is not hard.