280
Network-on-Chip
• Each router, selected for synthesis, should have one core mapped
onto it.
rs
∀ ∈ R, ∑ m =
r s
ci
1
ci∈C
• A core can be mapped to a router only when that router location
is selected for synthesis.
∀ s ∈ R sr s − m
r
≥ 0
r
,
c
s
i
• Router–core association constraints
s
• A core c i can be associated with the router at location r s (i.e., cl c
r
i
can be set to 1) if the physical distance (cdist c r ) is less than L MAX .
i s
,
s
∀ ∈ ∀ ∈
c i C, r s R cdist c r s × cl c
r
i
≤ L
i
MAX
• Now, mapping of a core onto a router is possible if there is a link
between them.
s
s
∀ ∈C, r ∈ R cl c
r
i
− m c
r
i
≥
c i
∀ s
,
0
• Inter-router link constraints
• Link can exist between routers, if the distance between them is
less than the maximum link length L MAX .
∀r i ∈ R, ∀r j ∈ R, i ≠ j , rdist r i rj × rl r i rj ≤ L MAX
• Constraints for core graph edges
• Each edge present in the core graph has to be mapped onto a
path in the evolved topology.
∀e i j ∈E , ∀ r s , r ∈ R, m
rs
+ m
rt
− P
r s rt
t
ci
cj
ci cj ≤ 1
and
2 × P c
rs rt
≤ m
rs
+ m
rt
i cj
ci
cj
• Path constraints
• To find the path between two router locations r s and r t , it is
required to identify the links and routers forming part of the
path. The following conditions are imposed for this purpose.
− Starting and ending routers must be part of the path.
∀e i j ∈ E , ∀ r s , r t ∈ R, P c
rs rt
i j
− n
rs rt
c
i
= 0