Lecture 18 Load Balancing and Vertex Cover.pdf - Comp 360 Algorithm Design(Fall 2017 Lecture 18 Load Balancing and Vertex Cover Instructor Yang Cai

Lecture 18 Load Balancing and Vertex Cover.pdf - Comp 360...

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Comp 360: Algorithm Design (Fall 2017) Lecture 18: Load Balancing and Vertex Cover Instructor: Yang Cai Basedon Kevin Wayne’sSlides.
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Coping with NP-completeness Q. Suppose I need to solve an NP -hard problem. What should I do? A. Sacrifice one of three desired features. i. Solve arbitrary instances of the problem. ii. Solve problem to optimality. iii. Solve problem in polynomial time. ρ -approximation algorithm. Guaranteed to run in poly-time. Guaranteed to solve arbitrary instance of the problem Guaranteed to find solution within ratio ρ of true optimum. Challenge. Need to prove a solution's value is close to optimum, without even knowing what optimum value is 2
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Load balancing Input. m identical machines; n jobs, job j has processing time t j . Job j must run contiguously on one machine. A machine can process at most one job at a time. Def. Let J ( i ) be the subset of jobs assigned to machine i . The load of machine i is L i = Σ j J(i) t j . Def. The makespan is the maximum load on any machine L = max i L i .
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