Efficient computation of an optimal switch sequence

Determine whether, for a noncollinear n-point set in the plane with assigned \pm 1 weights and switches corresponding to all connecting lines, one can efficiently compute a sequence of switches that produces a weight assignment of maximum signed discrepancy.

Background

Theorem 1 yields a polynomial-time factor-3 approximation for the maximum discrepancy, and the proof gives a cubic-time implementation based on repeatedly selecting a line incident to the maximum number of points. The exact optimization problem, however, asks for a switch sequence attaining the maximum possible discrepancy.

The paper explicitly poses the efficient exact-computation question, leaving unresolved whether an optimal sequence can be found efficiently.