FastRoute: An Efficient and High-Quality Global Router

Algorithm 1

3-bend routing algorithm.

(1)𝐶_best=+∞

(2)  For  𝑦= 0 to 𝑛−1

(3)   𝑑_ℎ(0,𝑦)=0

(4)   for  𝑥= 1 to 𝑚−1

(5)   𝑑_ℎ(𝑥,𝑦)=𝑑_ℎ(𝑥−1,𝑦)+cost_ℎ(𝑥−1,𝑦)

(6)  for  𝑥= 0 to 𝑚−1

(7)   𝑑_ℎ(𝑥,0)=0

(8)   for  𝑦= 1 to 𝑛−1

(9)      𝑑_𝑣(𝑥,𝑦)=𝑑_𝑣(𝑥,𝑦−1)+cost_𝑣(𝑥,𝑦−1)

(10) for  𝑦= 0 to 𝑛−1

(11)   for  𝑥= 0 to 𝑚−1

(12)      𝐵=(𝑥,𝑦)

(13)      𝑑_𝐿1(𝐵)=|𝑑_ℎ(𝑆)−𝑑_ℎ(𝑥,𝑦_𝑠)|+|𝑑_𝑣(𝑥,𝑦_𝑠)−𝑑_𝑣(𝐵)|

(14)      𝑑_𝐿2(𝐵)=|𝑑_ℎ(𝑆)−𝑑_ℎ(𝑥_𝑠,𝑦)|+|𝑑_𝑣(𝑥_𝑠,𝑦)−𝑑_𝑣(𝐵)|

(15)      𝑑_𝐿3(𝐵)=|𝑑_ℎ(𝑇)−𝑑_ℎ(𝑥,𝑦_𝑡)|+|𝑑_𝑣(𝑥,𝑦_𝑡)−𝑑_𝑣(𝐵)|

(16)      𝑑_𝐿4(𝐵)=|𝑑_ℎ(𝑇)−𝑑_ℎ(𝑥_𝑡,𝑦)|+|𝑑_𝑣(𝑥_𝑡,𝑦)−𝑑_𝑣(𝐵)|

(17)      Compute the cost of four possible 3-bend paths

       (i.e., L1–L3, L1–L4, L2-L3, L2–L4) from the four

       L-paths above plus via cost and compare them to

       𝐶_best. If better, update the best 3-bend path.