Parameters and
Variables
Definitions
D r r
s t
BW i
s
r
m ci
rs rt

P ci cj

j
The precalculated Manhattan distance between the routers r s and r t
The bandwidth requirement from core c i to core c j
s
r
Binary variable. m = 1 if core c i
ci
is mapped to the router r s; otherwise,
rs
m ci = 0.

s t
r r
Binary variable. P c = 1 if a path exists between routers r s and r t to which
i cj
s t
r
cores c i and c j have been mapped, respectively; otherwise, P
r
= 0.
ci cj
300
Network-on-Chip
10.3.6.1 Parameters and Variables
The parameters and variables used in the ILP formulation are noted in
Table 10.5.
10.3.6.2 Objective Function
The objective is to minimize the communication cost by selecting suitable
routers in the ReNoC for mapping and reconfiguration. The objective function can be formulated as follows: If cores c i and c j are mapped to routers
s t
r s and r t and a path exists between them in the network, P c
r
i
r
cj is equal to 1. This
multiplied by D r r gives the number of hops of the communication from c i
s t
to c j . The number of hops multiplied by bandwidth gives the communication
cost, which has to be minimized over all the edges in the core graph.
⎡
r r ⎤
s t
min
BW
r r t × P cj )
ci
⎣ ⎢∑ ei j ∈E
i j (∑ rs ,rt ∈R
D s
⎦ ⎥
10.3.6.3 Constraints
The following is the set of constraints framed to solve the mapping and
reconfiguration problem:
1. Mapping constraints
a. Each core has to be mapped onto only one router.
∑
s
∀ ∈ C,
m
r
i
= 1
c i
c
rs ∈R
b. Each router can have at most two cores mapped onto it.
∑
s
∀r s ∈ R,
m
r
i
≤ 2
c
ci ∈C
TABLe 10.5
Parameters and Variables of ILP Formulation