Geometric algorithms for a minimum cost assignment problem

We consider the minimum cost A-assignment problem, which is equivalent to the minimum weight one-to-many matching problem in a complete bipartite graph r = (A ,B), where A and B have n and k nodes respectively. Formulating the problem as a geometric problem, we give an qkn + k“n”’)-tirne randomized algorithm, which is better than existing qkt$ + n2 log n)-time algorithm if ks nob.