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Fig. 1.
The Integral of the Distance Over Time
Prob
(
M
i
,E
j
,Δt
)
≈
iDist
M
(
M
i
,E
j
,Δt
)
=
t
c
+
Δt
t
c
dist
M
(
M
i
.pos
(
t
)
,E
j
)
dt
=
1
2
. |V
k
| .
((
t
x
− t
c
)
2
+(
t
f
− t
x
)
2
)
.
3 Synthetically Considering Semantic, Time and Location
Factors
The traditional semantic cache approaches, have a limitation in that they cannot
satisfy the development of modern sensor grid technology. An advanced appli-
cation needs the new approach of semantic cache technology to synthetically
consider multiple factors. The main difference between semantic cache manage-
ment and a conventional semantic cache is the cost model, which should account
for several factors including semantic, location and time. Therefore, we need a
trade-off between those constraints [3].
Our approach is the comprehensive consideration of the semantic, time and
location balance of the 3-Dimensional vectors Nash Equilibrium. There is much
research on special algorithms for any special factors of 3
− D
factors. Our
approach has been developed for a Nash Equilibrium scheme with 3-Dimensional
vectors. Moreover we can generally and practically propose to any finite M-
Dimension vectors algorithm. Our algorithm is organically combined with these
3-D factors, and can be easily expanded.
3.1 To Define the Weights of the Nodes
W
i,j
=
α
i
W
i,j
+
β
i
W
i,j
+
γ
i
W
i,j
.
(2)
W
i,j
: the general weight of the semantic cache block
j
in the node
i
;
α
i
,
β
i
,
γ
i
: scalar coecient,
α
i
,β
i
,γ
i
∈ R
,
α
i
,β
i
,γ
i
≥
0, as
α
i
,β
i
,γ
i
<
0non-
sense;
W
i
=
F
i
∗
C
i
S
i
: the semantic weight;
W
i
=
L
: the life (time) weight;
W
i
=
2
. |V
k
| .
((
t
x
− t
c
)
2
+(
t
f
− t
x
)
2
): the location weight.
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