210 Energy-Aware Memory Management for EMSs
there are nine pairs of elements simultaneously alive, maximally distanced
from each other. Two such elements are, for instance, A[4][5]—produced in
the iteration (i =4,j = 5) and consumed in (i =14,j = 5), and A[14][4]—
produced in the iteration (i =14,j = 4) and consumed in (i =24,j = 4).
The distance between them in the linearization is 10 × 10 − 1 = 99. Finally,
if the rows are concatenated decreasingly [(A[index
1
][index
2
], index
2
=0, 9),
index
1
=18, 0], there are nine pairs of elements simultaneously alive as well,
(e.g., A[14][0] and A[4][9]), placed at the maximum distance 10×10 + 9 = 109.
For the other four linearizations, the maximum distances obtained have the
same values (i.e., 171, 181, 99, 109), ...