Question

Multi-processor Scheduling Input: (A, d, m), where A={a_(1),...,a_(n)} is a set of tasks, d is a deadline, and m is an element of Z is a number of processors. Each task a_(i) in A has an associated runtime a_(i).t. Accept if the tasks of A can be assigned to the m processors so that each processor can complete executing all tasks assigned to it before the deadline d. Prove that this is in NP and prove that it is NP complete by reducing any other NP-complete problem.

Name: multi processor scheduling input a d m where aa1an is a set of tasks d is a deadline and m is an element of z is a number of processors each task ai in a has an associated runtime ait ac 16513
Uploaded: 2023-11-01T05:04:22-08:00
Duration: 3 min 47 s
Channel: Akash M
Description: multi processor scheduling input a d m where aa1an is a set of tasks d is a deadline and m is an element of z is a number of processors each task ai in a has an associated runtime ait ac 16513

          Multi-processor Scheduling
Input: (A, d, m), where A={a_(1),...,a_(n)} is a set of tasks, d is a
deadline, and m is an element of Z is a number of processors. Each task a_(i) in A
has an associated runtime a_(i).t.
Accept if the tasks of A can be assigned to the m processors so that
each processor can complete executing all tasks assigned to it before
the deadline d. Prove that this is in NP and prove that it is NP complete by reducing any other NP-complete problem.

Added by Anna J.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Akash M

11/01/2023

Step 1

Step 1: To prove that the problem is in NP, we need to show that given a solution, we can verify it in polynomial time. Show more…

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Multi-processor Scheduling Input: (A, d, m), where A={a_(1),...,a_(n)} is a set of tasks, d is a deadline, and m is an element of Z is a number of processors. Each task a_(i) in A has an associated runtime a_(i).t. Accept if the tasks of A can be assigned to the m processors so that each processor can complete executing all tasks assigned to it before the deadline d. Prove that this is in NP and prove that it is NP complete by reducing any other NP-complete problem.