Placing Multimode Streaming Applications on Dynamically Partially Reconfigurable Architectures

Algorithm 2

Merging two paths 𝑝_𝑖 and 𝑝_𝑖 according to common sequence 𝑆_𝑖,𝑗 and adding them to the merged graph 𝐺_𝑀.

(1): ensure 𝐺_𝑀 contains the NOP nodes 𝑁𝑂𝑃₀ and 𝑁𝑂𝑃_𝑛;

(2): 𝑣₀=𝑁𝑂𝑃₀

(3): for   𝑘=0  to   |𝑆_𝑖,𝑗|   do

(4):  (𝑣_𝑖^(𝑘),𝑣_𝑗^(𝑘))=𝑆_𝑖,𝑗[𝑘]; // the 𝑘-th pair in the sequence

(5): determine or-paths 𝑜𝑟_𝑖/𝑗, that is, all vertices in 𝑝_𝑖/𝑗 between 𝑣^(𝑘−1)_𝑖/𝑗 and 𝑣^(𝑘)_𝑖/𝑗

(6): add 𝑜𝑟_𝑖/𝑗 to 𝐺_𝑀; // see Algorithm 3

(7): make new node 𝑛_𝑀;

(8): link   𝑣_𝑀[𝑖] to 𝑣_𝑖^(𝑘) and 𝑛_𝑀[𝑗] to 𝑣_𝑗^(𝑘);

(9):      add   𝑣_𝑀 to 𝐺_𝑀;

(10):   add edge to 𝐺_𝑀 connecting the last vertices added from 𝑝_𝑖 and 𝑝_𝑗 to 𝑣_𝑀;

(11): 𝑣₀=𝑣_𝑀;

(12): end for