The A-complete Matching Problem

The matching problem with preference order has a wide range of practical applications in our real life.In order to establish a fair and reasonable matching mechanism,we consider two types of the A-complete matching problem.Firstly,we address the popular A-complete matching problem,which is defined as follows.We are given a bipartite graph G=(A ?B,E;r)where the vertices in A are called applicants and the vertices in B are called posts,the E is a set of edges and the r:E? R+is a rank function.Each vertex has a preference list ranking its neighbors in a strict order of preference.For all a? A,if ab,ab'? E and r(ab)