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- W2884202064 abstract "We consider the classic scheduling problem of minimizing the total weighted flow-time on a single machine (min-WPFT), when preemption is allowed. In this problem, we are given a set of n jobs, each job having a release time rj, a processing time pj, and a weight wj. The flow-time of a job is defined as the amount of time the job spends in the system before it completes; that is, Fj = Cj − rj, where Cj is the completion time of job. The objective is to minimize the total weighted flow-time of jobs.This NP-hard problem has been studied quite extensively for decades. In a recent breakthrough, Batra, Garg, and Kumar [6] presented a pseudo-polynomial time algorithm that has an O(1) approximation ratio. The design of a truly polynomial time algorithm, however, remained an open problem. In this paper, we show a transformation from pseudo-polynomial time algorithms to polynomial time algorithms in the context of min-WPFT. Our result combined with the result of Batra, Garg, and Kumar [6] settles the long standing conjecture that there is a polynomial time algorithm with O(1)-approximation for min-WPFT." @default.
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- W2884202064 date "2019-01-06" @default.
- W2884202064 modified "2023-09-26" @default.
- W2884202064 title "A polynomial time constant approximation for minimizing total weighted flow-time" @default.
- W2884202064 doi "https://doi.org/10.5555/3310435.3310531" @default.
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