1. Interval scheduling. Assume that we are given jobs, and for each job we know the start and the finish times, and , respectively. Two jobs are compatible if they do not overlap. Find maximum subset of mutually compatible jobs. Provide an analysis of complexity for the algorithm.

2. Provide an algorithm for determining a maximum spanning tree in an undirected graph with positive edge weight. Provide an analysis of complexity of the algorithm.

3. Interval partitioning. Assume that we are given lectures, and for each lecture we know the start and the finish times, and , respectively. Find the minimum number of classrooms to schedule all lectures, so that no two lectures occur at the same time in the same room. Provide an analysis of complexity for the algorithm.