1. Suppose you are a consultant who specializes in improving performance in rigid corporations with dysfunctional cultures. In particular, suppose that you are serving companies in which employees habitually ignore e-mails and only respond to directions given in face-to-face, one- on-one meetings with their direct managers. One service you wish to provide is to improve the speed with which new directives propagate through the organization by prioritizing the order of the meetings each manager holds. We suppose that each meeting takes a fixed amount of time, and that once an employee has received their directions, they begin notifying their direct reports in the order that you specify to them. So, the CEO notifies their first subordinate; then the first subordinate notifies their own first subordinate while the CEO notifies their second subordinate; then the first subordinate of the first subordinate notifies their own first subordinate at the same time that the first subordinate notifies their second subordinate and that the CEO notifies their third subordinate, and so on. You aim to specify an ordering of each employee's subordinates such that the total number of rounds of meetings for the entire organization to receive the new directions is minimized. Concretely, we