Approximation Algorithms Performance Guaranteed

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Approximation Algorithms(Performance Guaranteed)

• For your information and enjoyment only.
• Not included in the Final Exam of UIT2201

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Approximation Algorithms(Performance Guaranteed)

• If we cannot find the best solution quickly,
• we will settle for a good enough solution
• but, we dont want it to be too bad
• Approximation Algorithms Not optimal solution,
• but with some performance guarantee
• (eg, no worst than twice the optimal)
• Even though we dont know what the optimal
  solution is!!!

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Approximation Algorithms(Performance Guaranteed)
Bin Packing Problem

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.5 .7 .5 .2 .4 .2 .5 .1 .6
Optimal Packing
N0 4
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Approximation Algorithms(Performance Guaranteed)
Bin Packing Problem
.5 .7 .5 .2 .4 .2 .5 .1 .6
.1
N0 4
Next Fit Packing Algorithm
N 6
5
Next Fit Packing Algorithm
Let a1 a2 .. ? 2 ? ? N 1
N0 ? ? ? ?
a1.. ai gt 1 ai.. aj gt 1 aj.. ak gt
1 al.. am gt 1
. . . . .
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Approximation Algorithms(Performance Guaranteed)
.5 .7 .5 .2 .4 .2 .5 .1 .6
Next Fit Packing Algorithm
First Fit Packing Algorithm
N 5
(Proof omitted)