Hardware Accelerated Sequence Alignment with Traceback

Algorithm 1

Procedure for TracePartial.

procedure TracePartial(𝐴,𝐵,𝑚,𝑛,𝑅,𝐸)

{

 𝑥₂←𝑚,𝑦₂←𝑛

 while (𝑥₂>1) do

  𝑥₁←⌊(𝑥₂−1)/𝑊⌋⋅𝑊+1

  𝑦₁←(𝑥₁>1⋀𝑦₂≥1)?𝑅[𝑥₂,𝑦₂]+1∶1

  𝑥𝑙𝑒𝑛←𝑥₂−𝑥₁+1,𝑦𝑙𝑒𝑛←𝑦₂−𝑦₁+1

  if (𝑦𝑙𝑒𝑛=0) then

   Add 𝑥𝑙𝑒𝑛 DELETE operations to 𝐸^′

  else if (𝑦𝑙𝑒𝑛≤𝑌) then

   ScanFull(𝐴_𝑥1,𝐵_𝑦1,𝑥𝑙𝑒𝑛,𝑦𝑙𝑒𝑛,𝑇)

   TraceFull(𝐴_𝑥1,𝐵_𝑦1,𝑥𝑙𝑒𝑛,𝑦𝑙𝑒𝑛,𝑇,𝐸^′)

  else // interchange 𝐴 and 𝐵

   ScanPartial(𝐵_𝑦1,𝐴_𝑥1,𝑦𝑙𝑒𝑛,𝑥𝑙𝑒𝑛,𝑅^′)

   TracePartial(𝐵_𝑦1,𝐴_𝑥1,𝑦𝑙𝑒𝑛,𝑥𝑙𝑒𝑛,𝑅^′,𝐸^′)

   ∀𝑒∈𝐸^′: replace DELETE ⇔ INSERT

  end if

  𝐸←𝐸∪𝐸^′

  𝑥₂←𝑥₁−1,𝑦₂←𝑦₁−1

 end while

}