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15
Limits to Computation
15.1
This reduction provides an upper bound of
O(
n
log
n
)
for the problem of
maximum
f
nding (that is the time for the entire process), and a lower bound
of constant time for SORTING (since that is the time spent by Maximum
Finding in this process). Neither bound is particularly enlightening. There is
no true reduction from SORTING to Maximum Finding (in the sense that the
transformations do not dominate the cost) since SORTING is an intrinsicly
more dif
f
cult problem than Maximum Finding.
15.2
Consider the following fact:
"
AB
00
#
2
=
"
A
2
AB
#
.
Thus, if we had an algorithm that could square an
n
×
n
matrix in less time
than needed to multiply two matrices, we could use a transformation based
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This note was uploaded on 12/27/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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