Geometric separability using orthogonal objects

•An efficient algorithm for bichromatic separability for rectangular and square annuli.•Objective is to minimize the width of axis-parallel rectangular and square annulus.•Geometric separability using orthogonal annuli in fixed and arbitrary orientation.•Separability problem using orthogonal convex polygon with minimum number of edges.•Efficient Polynomial-time algorithms to find separating annuli with a minimum width.