k-ary n-cube (Torus) k-ary n-mesh (Mesh)
bisection boundhop count bound
Two-level packaging (k even)
router serialization wire
k-ary 1-cube
0 1
nk
2 k
k-ary 1-mesh
0 1 2 k
Two-level packaging (k even)
0
3
1
2
Folding to eliminate long channels
from a torus layout.
k-ary
(n-1)-cube
k-ary
(n-1)-cube
k-ary
(n-1)-cube
k
n–1
channels
Recursive construction of higher
dimensional k-ary n-cubes.
uniform
traffic
Topology
H
min
B
C
w
Θ
ideal
NH
min
=
b
γ
max
γ
max
γ
max
γ
max
C
>
2B
C
>
N
T
0
=H
min
t
r
L
b
D
min
υ
+
+
4
k
8
4
n
(
k
4k
1
)
k even
k odd
k even
k odd
=
=
=
k
k
8
1
8k
4k
n–1
4N
=
b
T
s
L
δ=4n
b=wf
<
min
W
n
kW
s
4n
4N
Θ
ideal
=
8b
nk
uniform
traffic
H
min
B
C
w
γ
max
4
k
4
3
n
(
k
3k
1
)
k even
k odd
k even
k odd
=
=
=
=
=
k
k
4
1
4k
2k
n–1
2N
=
T
s
L
δ=4n
b=wf
<
min
W
n
kW
s

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