Motivated by networks interplay, we study the problem of computing monochromatic plane matchings in bicolored point set. Given a bicolored set P of n red and m blue points in the plane, where n and m are even, the goal is to compute a plane matching M R of the red points and a plane matching M B of the blue points that minimize the number of crossing between M R and M B as well as the longest edge in M R ∪ M B . In this paper, we give asymptotically tight bound on the number of crossings between M R and M B when the points of P are in convex position. Moreover, we present an algorithm that computes bottleneck plane matchings M R and M B , such that there are no crossings between M R and M B , if such matchings exist. For points in general position, we present a polynomial-time approximation algorithm that computes two plane matchings with linear number of crossings between them.
Abu-Affash, Bhore and Carmi in REF examined bicolored matchings that minimize the number of crossings between edges matching different color sets.
Monochromatic plane matchings in bicolored point set
Inf. Process. Lett.
Inf. Process. Lett.
Mathematics Computer Science