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Does an algorithm exist to check for the existence of a Real-Time Multiprocessor Schedule for aperiodic hard tasks(all of which have the same Release time)?

Assumptions:

  • The processors are Uniform parallel machines
  • Job preemption is permitted
  • Job migration is permitted
  • Job parallelism is forbidden

EDIT: Let there be $n$ jobs $J = \{j_1, j_2,\text{...}, j_n\}$ and $m$ no of processors $P = \{p_1, p_2,\text{...}, p_m\}$. Each job $j_i$ has a task time $t_i$(amount of work it would take to complete it) and due time $d_i$. Each processor has a constant speed $s_i$(amount of work it does per unit time). Each task must be completed before its due time.

I am interested to know about an algorithm with can check feasibility of a schedule in polynomial time.

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  • $\begingroup$ An algorithm probably exists – I suspect you're interested in an efficient algorithm. $\endgroup$ – Yuval Filmus Dec 4 '17 at 22:05
  • $\begingroup$ Can you specify your problem in more details? $\endgroup$ – Yuval Filmus Dec 4 '17 at 22:05
  • $\begingroup$ @YuvalFilmus I added some more details. Let me know if you want me to clarify more. $\endgroup$ – Nilesh Hirani Dec 4 '17 at 22:15
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Y. Cho and S. Sahni, Scheduling Independent tasks with due times on a uniform Processor System, Jr. of the ACM, 1980

Presents an algorithm to preemptively schedule n tasks(with due dates) on m uniform processors whenever a solution exists in $O(n\log{n} + mn)$ time.

Which is a stronger problem than I wanted to solve but still gives a polynomial algorithm, which answers my question.

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