New Three-Level Resource Management Enhancing Quality of Offline Hardware Task Placement on FPGA

Algorithm 3

Branch and Bound for hardware task placement [24].

𝑐: narural // the counter on branched nodes

b: natural // the number of branched nodes provided by the current node

Best 𝐹=+00,

Live = {(Nodeinrootlevel,𝐹(nodeinrootlevel))}// the set of nodes to be processed

while Live ≠⊘  do

 Select the node N from Live to be processed which gives the best F by using DFS

 Live = Live⧵{(𝑁,𝐹(𝑁))}

 if  F(N) = F(X) for a feasible complete solution X and F (X) < Best F then

  Best 𝐹=𝐹(𝑋)

  Solution =X // A complete solution is founded

 else if 𝐹(𝑁)≥ Best F then

  Discard N from processing // partial candidate is rejected

 else

  // partial candidate is kept

  Branch on N generating 𝑁1,…,𝑁𝑏 by respecting the problem constraints

  for 𝑐=1  to  𝑏  do

   Bound Nc: compute F(Nc) // bound calculation for the node Nc

   Live = Live U {(𝑁𝑐,𝐹(𝑁𝑐)}

  end for

 end if

end while

Optimal Solution = Solution, Optimal Value = Best 𝐹