Question: 3. (20 points) Show that (a) P3 || Cmax is NP-hard by showing the decision version of P3 || Cmax is NP-complete. (Hint: Use PARTITION

3. (20 points) Show that (a) P3 || Cmax is NP-hard

3. (20 points) Show that (a) P3 || Cmax is NP-hard by showing the decision version of P3 || Cmax is NP-complete. (Hint: Use PARTITION as the source problem in the reduction) (b) Pm || Cmax is NP-hard for fixed m> 3 by showing the decision version of Pm || Cmax is NP-complete. (Hint: Also use PARTITION as the source problem in the reduction. Generalize the reduction given in part (a).) 3. (20 points) Show that (a) P3 || Cmax is NP-hard by showing the decision version of P3 || Cmax is NP-complete. (Hint: Use PARTITION as the source problem in the reduction) (b) Pm || Cmax is NP-hard for fixed m> 3 by showing the decision version of Pm || Cmax is NP-complete. (Hint: Also use PARTITION as the source problem in the reduction. Generalize the reduction given in part (a).)

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