Georgetown Admissions Process and Bipartite Graphs
In class we discussed the relevance of the Bipartite Graphs, matching and perfect matching. In a bipartite graph, nodes are split into two categories, and each edge connects a node from one category to a node in the other category. From this graph comes two other principles that I want to discuss: matching and perfect matching. Matching refers to a subset of edges where each node is connected to at most one other node. Not all nodes need to matched to qualify to under the matching definition. On the other hand, perfect matching is when there are an equal number of nodes on each side of a bipartite graph. A perfect matching exists “when each node is connected by an edge to the node it is assigned to, and no two nodes on the left are assigned to the same node on the right.”
To analyze this networking theorem it is easier to consider real life applications rather than nodes. This principle can be applied to students and dorm rooms, courses and instructors, sellers and buyers, etc. I am going to delve into the application involving students and colleges; a frightening process most students will undergo. Universities unknowingly utilize this bipartite graph when attempting to match each students application with their school, however a perfect match is not achieved because not each student is accepted, therefore an edge from one node to another may not exist. Also, there are not an equal number of students and universities, again violating the perfect match definition. From the student’s perspective, likewise a perfect match is hard to achieve because it is likely that students will be rejected from their top schools depending on their academics, therefore an edge will not exist. Because perfect matching does not exist at all times during this process it can be stated that there is a constricted set. This is because either the university or students edges to the other side of the bipartite graph constrict the formation of a perfect matching.
I recently read an article discussing how Georgetown was going to pursue the admissions process in the upcoming years. They are now giving preferential status to descendants of the enslaved. This new preferential status will create more constricted sets, causing more students (those not descendants of the enslaved) to get rejected from their desired school. It is interesting to analyze how the preference of minorities affects and further, creates more constricted sets on students not in the minority.
Source: http://www.nytimes.com/2016/09/02/us/slaves-georgetown-university.html?_r=0