
102 Energy-Aware Memory Management for EMSs
iterators are increasing with the step size of 1). The iterator vector j is larger
lexicographically than i (written j i)if(j
1
>i
1
), or (j
1
= i
1
and j
2
>i
2
),
...,or(j
1
= i
1
,... ,j
n−1
= i
n−1
, and j
n
>i
n
). The minimum/maximum
iterator vector from a set of such vectors is the smallest/largest vector in the
set relative to the lexicographic order. For instance, in the loop nest
for (i=0; i<=3; i++)
for (j=0; j<=3; j++)
for (k=0; k<=3; k++) ··· A[i+j+k] ···
the maximum iterator vector such that the element, say, A[5] be accessed is
[ijk]
T
max
=[320]
T
, while the minimum iterator vector is [0 2 3]
T
. Sec-
tion 3.5.3 will