Interval Scheduling Optimality of greedy with EFT Another standard method is induction Both ir+1 and jr+1 were compatible with the previous selection (1=1,..., ir = jr) ➤ Consider the solution i₁, 2, ..., ir, ir+1, Jr+2, ..., Jm o It should still be feasible (since fir ⚫ It is still optimal fir+z) ⚫ And it matches with greedy for one more step (contradiction!) Greedy: OPT: J: job finishes before J J+s From the following chose the correct answer: a. When we replace J₁+1 with i+₁ in OPT, we are guaranteed i₁ is not selected as a job in OPT b. When we replace Jr+1 with i√+1 in OPT, i++₁ maybe selected as a job in OPT with index greater than Jr+1 c. When we replace Jr+1 with Ir+₁ in OPT, I++₁ maybe selected as a job in OPT with index smaller than Jr+1 d. None of the above

Interval Scheduling Optimality of greedy with EFT Another standard method is induction Both ir+1 and jr+1 were compatible with the previous selection (1=1,..., ir = jr) ➤ Consider the solution i₁, 2, ..., ir, ir+1, Jr+2, ..., Jm o It should still be feasible (since fir ⚫ It is still optimal fir+z) ⚫ And it matches with greedy for one more step (contradiction!) Greedy: OPT: J: job finishes before J J+s From the following chose the correct answer: a. When we replace J₁+1 with i+₁ in OPT, we are guaranteed i₁ is not selected as a job in OPT b. When we replace Jr+1 with i√+1 in OPT, i++₁ maybe selected as a job in OPT with index greater than Jr+1 c. When we replace Jr+1 with Ir+₁ in OPT, I++₁ maybe selected as a job in OPT with index smaller than Jr+1 d. None of the above

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