Chapter 7 Linear Programming

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Chapter 7Linear Programming

• (2) Rounding

Ding-Zhu Du
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Rounding

• Combinatorial Rounding
• vertex-cover
• scheduling on unrelated parallel machine
• Random Rounding
• Maximum satisfiability

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Vertex Cover
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LP-Relaxation
Rounding
Theorem
Proof.
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Half-integerality
Theorem
Proof
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Scheduling on UPM
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LP-Relaxation
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Combinatorial Property of x
Bipartite graph H
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Rounding
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Prune
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How to find T?
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Proof of the Combinatorial Property
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Important Facts
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Max Sat
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LP-relaxation
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Random Variables
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Calculation of E(Z)
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Lower bound of E(Zj)
Lemma
Proof
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0
1
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Lower Bound for EZF
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Random Rounding
Theorem
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Thanks, End