algorithm - Is this MSP an instance of the TSP? -

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in book, the algorithm design manual, steven s. skiena poses following problem:

            enter image description here

now consider following scheduling problem. imagine highly-indemand actor, has been presented offers star in n different movie projects under development. each offer comes specified first , last day of filming. take job, must commit being available throughout entire period. cannot simultaneously accept 2 jobs intervals overlap.

for artist such yourself, criteria job acceptance clear: want make money possible. because each of these films pays same fee per film, implies seek largest possible set of jobs (intervals) such no 2 of them conflict each other.

for example, consider available projects in figure 1.5 [above]. can star in @ 4 films, namely “discrete” mathematics, programming challenges, calculated bets, , 1 of either halting state or steiner’s tree.

you (or agent) must solve following algorithmic scheduling problem:

problem: movie scheduling problem

input: set i of n intervals on line.

output: largest subset of mutually non-overlapping intervals can selected i?

i wonder, instance of tsp (perhaps simplified one)?

this problem can solve choosing film earliest finish date, , proceeding there, o(n^2) process (there may faster solutions). since we've found polynomial time solution, it's not instance of tsp, unless: (1) p=np, , (2) there's embarrassingly easy proof of (1).


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