A DAG Scheduling Scheme on Heterogeneous Computing Systems Using Tuple-Based Chemical Reaction Optimization

Algorithm 1

CEFT.

(1)    //PHASE 1: Find the constrained critical paths (CCPs)

(2)    Find set of critical paths CP according to the description in the second paragraph of Section 3.1.

(3)    𝑗 = 1

(4)    for  𝑖 = 1 to |CP|  do

(5)             while there exist ready nodes in CP_𝑖  do

(6)                   Insert ready node 𝑣_𝑘 into constrained critical path Queue (𝑄_𝑗).

(7)             end while

(8)             𝑗← 𝑗 + 1

(9)             𝑖← 𝑖%|CP|

(10)  end for

(11)  //PHASE 2: Assign and schedule tasks

(12)  for  𝑗 = {1, 2, …, |𝑄|} do

(13)          for  each processor 𝑃_𝑟∈𝑃 do

(14)                 for  each node 𝑤∈𝑄_𝑗 do

(15)                       Find the start time of node 𝑘, which is the predecessor of 𝑤

                                 ST_𝑃𝑟(𝑤, 𝑘) = maxAEFT_𝑘+CM𝑤,𝑃_𝑟,𝑘,𝑃_𝑥,AT_𝑃𝑟

(16)                       Find the finish time of the node

                                EFT_𝑃𝑟(𝑤) = maxST_𝑃𝑟(𝑤,𝑘)_{∀𝑘∈Pred(𝑤)} + EC_𝑃𝑟(𝑤)

(17)                 end for

(18)                 Find the finish time of the CCP 𝑄_𝑗

                          CEFT_𝑃𝑟(𝑄_𝑗) = maxEFT_𝑃𝑟(𝑤)_{∀𝑤∈𝑄𝑗}

(19)           end for

(20)         Assign the processor to CCP 𝑄_𝑗 which minimizes CEFT_𝑃𝑟(𝑄_𝑗).

(21)          Let 𝑃_𝑥 be assigned, update AEFT_𝑤 of each task 𝑤 in 𝑄_𝑗

                   (AEFT_𝑤)_{∀𝑤∈𝑄𝑗}=(EFT_𝑃𝑥(𝑤))_{∀𝑤∈𝑄𝑗}

(22) end for