275
Application-Specific Network-on-Chip Synthesis
• If a core node is mapped to a port of a router, all traffic emanating
from that node must enter into that port. The same is the case for
a destination node. Hence, for each router r k , for all p k,l and for all
(v i , v j ) in E, I i , j, k , l ≥ NR i ,k , l and O i , j, k , l ≥ NR j,k , l
• If a core node is mapped to a port of a router, no traffic from any
other port can enter or leave that port.
∀(v i , v j )∈E, ∀v m ∈ V, m ≠ i, m ≠ j,∀p k ,l
NR m ,k , l + I i , j, k , l ≤ 1 and NR m ,k , l + O i , j, k , l ≤ 1
• If a traffic enters a port of a router, it should not enter from any
other port of that router. The same is true for a traffic leaving a
port of a router. The constraint ensures that the traffic does not get
split across multiple ports. For each router r k and for all (v i , v j )  ∊  E,
∑ I i , j, k ,l ≤
1 and ∑ O i , j, k , l ≤ 1
∀pk l
,
• If a traffic enters a port of a router, it has to leave exactly one of
the other ports of that router. Similarly, if a traffic leaves a port
of a router, it must have entered from exactly one of the other
ports of the router. The constraint conserves the flow of traffic.
For each router r k , for all p k,l and for all (v i , v j ) ∊ E,
O
≥ I , , and
I
≥ O , ,
i j k m
, , ,
i j k l
,
i j k m
, , ,
i j k l
,
∑
∑
∀ ,
∀p ,
pk m m
, ≠l
k m m
, ≠l
• If two ports of different routers are connected, a traffic leaving
from one port should enter the other and vice versa (assuming
bidirectional links). For each pair of routers {r k , r m }, k ≠ m, for all
p k,l , for all p m,n , and for all (v i , v j ) ∊ E,
, ,
+ i j k l O , , , ≤ 1 and RR , ,
i j k l
O , , , ≤ 1
RR k l m n
,
I , , , − i j m n
k l m n
, − I , , , + i j m n
• If two different ports are connected, a traffic can leave exactly
one of the two ports. Similarly, a traffic can enter only one of the
two ports. For each pair of routers {r k , r }, k ≠ m, for all p k,l , for all
m
p m,n , and for all (v i , v j ) ∊ E,
RR k l m n
, + I i j k l
, , , + I , , , ≤ 2 and RR k l m n
, + O , , , + O i j m n ≤ 2
, ,
i j m n
, ,
i j k l
, , ,
• If a traffic enters a port of a router, the port must be mapped to a
core node or to a port of a different router. That is, if I i,j,k,l is 1 for some
(v i , v j ) ∊ E, some NR i,k,l should be 1, or some RR m,n,k,l should be 1, where
∀pk l
,