270
Network-on-Chip
Y i,min ≥ Y j,max
Y j,min ≥ Y i,max
Therefore,
DX i , j + DX j , i + DY i , j + DY j , i ≥ 1
• The layout should satisfy the aspect ratio constraints. Thus,
Y max ≥ γ min × X max
Y max ≤ γ max × X max
• The layout should not violate X and Y boundaries. Thus, for each
node v i ∊ V,
X i,max ≤ X max
and
Y
≤ Y max
i,max
9.4.4 Constraints for Mesh Topology
The cores in a mesh topology are aligned along a grid. The height and width
of a grid are determined by the largest core in that particular row or column,
respectively. Hence, we need additional constraints to restrict the start positions of cores at some valid grid points only. Figure 9.1a shows a valid mesh
floorplan, whereas 9.1b is an invalid one.
j
i
(a)
(b)
Figure 9.1
(a) Valid mesh-based floorplan; (b) illegal layout of mesh-based topology. (Redrawn from
Srinivasan, K., et   al., IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 14(4),
407–420, 2006.)