Approximation of convex curves with application to the Bicriterial Minimum Cost Flow Problem

An approximation of an explicitly or implicitly given convex curve in the plane is given by two piecewise linear ‘outer’ and ‘inner’ curves. To compute these, three rules for choosing the supporting points are proposed and it is shown for two of them that the projective distance between inner and outer approximation decreases quadratically with the number of supporting points. This method is applied to approximate the efficient point curve of the Bicriterial Minimum Cost Flow Problem, which is a piecewise linear convex curve that may have an exponential number of breakpoints in the worst case.