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Mathematics of Operations Research
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The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders
Mathematics of Operations Research
Vertex cover in graphs with locally few colors
Information and Computation
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We present a new linear programming relaxation for the problem of minimizing the sum of weighted completion times of precedence-constrained jobs. Given a set of n jobs, each job j has processing time p"j and weight w"j. There is also a partial order @? on the execution of the jobs: if j@?k, job k may not start processing before job j has been completed. For C"j representing the completion time of job j, the objective is to minimize the weighted sum of completion times, @?"jw"jC"j. The new relaxation is simple and compact, has exactly two variables per inequality and half-integral extreme points. An optimal solution can be found via a minimum cut computation, which provides a new 2-approximation algorithm in the complexity of a minimum cut on a graph. As a by-product, we also introduce another new 2-approximation algorithm for the problem.