Complexity-1

# Complexity-1 - Complexity and Scheduling IEE 533...

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Complexity and Scheduling IEE 533 [email protected]

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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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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.

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Complexity-1 - Complexity and Scheduling IEE 533...

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