Let S be a set of n points in general position in the plane, r of which are red and b of which are blue. In this paper we present algorithms to find convex sets containing a balanced number of red and blue points. We provide an O (n(4)) time algorithm that for a given alpha is an element of [0, 1/2] finds a convex set containing exactly inverted right perpendicular alpha rinverted left perpendicular red points and exactly inverted right perpendicular alpha inverted left perpendicular blue points of S. If inverted right perpendicular alpha rinverted left perpendicular + inverted right perpendicular alpha binverted left perpendicular is not much larger than 1/3n, we improve the running time to O (n logn). We also provide an O (n(2) logn) time algorithm to find a convex set containing exactly inverted right perpendicularr+1/2inverted left perpendicular red points and exactly inverted right perpendicularb+1/2inverted left perpendicular blue points of S, and show that balanced islands with more points do not always exist.
