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View Full Document Introduction to
Computational Complexity
Menkes van den Briel
Arizona State University
Department of Industrial Engineering
The Importance of Complexity
Problem Size
Run
Time
n=10
n=20
n=30
n=40
n=50
n=60
n
0.00001
seconds
0.00002
seconds
0.00003
seconds
0.00004
seconds
0.00005
seconds
0.00006
seconds
n
2
0.0001
seconds
0.0004
seconds
0.0009
seconds
0.0016
seconds
0.0025
seconds
0.0036
seconds
n
3
0.001
seconds
0.008
seconds
0.027
seconds
0.064
seconds
0.125
seconds
0.216
seconds
n
5
0.1
seconds
3.2
seconds
24.3
seconds
1.7
minutes
5.2
minutes
13.0
minutes
2
n
0.001
seconds
1.05
seconds
17.90
minutes
12.73
days
35.70
years
365.59
centuries
3
n
0.059
seconds
58.11
minutes
6.53
years
3855
centuries
2.3E+08
centuries
1.3E+13
centuries
Complexity
n
n
2.8
hours
3.3E+10
centuries
6.5E+28
centuries
3.8E+48
centuries
2.8E+69
centuries
1.5E+91
centuries
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View Full Document Effects of New Technology
Present
Computer
100 Times
Faster
1000 Times
Faster
n
N
1
100 N
1
1000 N
1
n
2
N
2
10 N
2
31.6 N
2
n
3
N
3
4.64N
3
10 N
3
n
5
N
4
2.5 N
4
3.98 N
4
2
n
N
5
N
5
+ 6.64
N
5
+ 9.97
3
n
N
6
N
6
+ 4.19
N
6
+ 6.29
n
n
N
7
l
A
problem
is a general question to be answered, usually
possessing several parameters, or free variables, whose
values are left unspecified.
P2  rj, prec  TWC
l
An
instance
of a problem is obtained by specifying
particular values for all the problem parameters.
What variable values must be
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This note was uploaded on 10/07/2011 for the course IEE 533 taught by Professor Johnfowler during the Spring '10 term at ASU.
 Spring '10
 JohnFowler

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