Is this MSP an instance of the TSP?

Question

In his book, The Algorithm Design Manual, Steven S. Skiena poses the following problem:

            

Now consider the following scheduling problem. Imagine you are a highly-indemand actor, who has been presented with offers to star in n different movie projects under development. Each offer comes specified with the first and last day of filming. To take the job, you must commit to being available throughout this entire period. Thus you cannot simultaneously accept two jobs whose intervals overlap.

For an artist such as yourself, the criteria for job acceptance is clear: you want to make as much money as possible. Because each of these films pays the same fee per film, this implies you seek the largest possible set of jobs (intervals) such that no two of them conflict with each other.

For example, consider the available projects in Figure 1.5 [above]. We can star in at most four films, namely “Discrete” Mathematics, Programming Challenges, Calculated Bets, and one of either Halting State or Steiner’s Tree.

You (or your agent) must solve the following algorithmic scheduling problem:

Problem: Movie Scheduling Problem

Input: A set I of n intervals on the line.

Output: What is the largest subset of mutually non-overlapping intervals which can be selected from I?

I wonder, is this an instance of the TSP (perhaps a simplified one)?

Answer 1

This problem can be solve by simply choosing the film with the earliest finish date, and proceeding from there, an O(n^2) process (there may be even faster solutions). Since we've found a polynomial time solution, it's not an instance of TSP, unless: (1) P=NP, and (2) there's an embarrassingly easy proof of (1).