A computing company is running a set of processes every day. Each process has its own start time and finish time, during which it runs continuously. The company has developed a process_check module, that runs briefly (consider this to take just 1 point in time) and records important pieces of information about the processes running at that time. The company would like to run the process_check module as few times as possible each day, while making sure that the module is called at least once during the execution of each process. Give an efficient algorithm that based on the start and finish time of each process will find the smallest set of possible moments of time at which to run the process_check module (making sure that the module is invoked at least once for each process).

Note: to prove that your greedy strategy yields the optimal solution, you have to prove that the problem has the greedy-choice property.