Meta-Algorithms for Scheduling a Chain of Coarse-Grained Tasks on an Array of Reconfigurable FPGAs

Algorithm 4

SPRM (dynamic-node generation) algorithm.

COST(𝑛)

{Compute minimum cost using dynamic programming}

(1) for 𝑙=𝑛−1 down to 0 do // 𝑛 is number of tasks in chain

(2)  𝑐𝑜𝑠𝑡[𝑙]=∞

(3) if (𝑛−𝑙) ≤ 𝑘−𝑏[𝑙]−𝑏[𝑛−1] then //Base case

(4)   𝑐𝑜𝑠𝑡[𝑙]=0

(5)   𝑓𝑖𝑟𝑠𝑡𝐶𝑢𝑡[𝑙]=𝑛

(6) else // General case

(7)  for 𝑖 in [0,𝑘−1−𝑏[𝑙]] do // try all cuts, determine best one

(8)   if 𝑖<𝑘−1−𝑏[𝑙] or 𝑏[𝑙+𝑖]=0 then // checks whether additional task needed

(9)     𝑡𝑒𝑚𝑝𝐶𝑜𝑠𝑡=cost[𝑙+𝑖+1]+𝐶_𝑙+𝑖+1

(10)   if 𝑡𝑒𝑚𝑝𝐶𝑜𝑠𝑡<𝑐𝑜𝑠𝑡[𝑙] then

(11)      𝑐𝑜𝑠𝑡[𝑙]=𝑡𝑒𝑚𝑝𝐶𝑜𝑠𝑡

(12)     𝑓𝑖𝑟𝑠𝑡𝐶𝑢𝑡[𝑙]=𝑙+𝑖+1

end