6,335 research outputs found
The Complexity of Mean Flow Time Scheduling Problems with Release Times
We study the problem of preemptive scheduling n jobs with given release times
on m identical parallel machines. The objective is to minimize the average flow
time. We show that when all jobs have equal processing times then the problem
can be solved in polynomial time using linear programming. Our algorithm can
also be applied to the open-shop problem with release times and unit processing
times. For the general case (when processing times are arbitrary), we show that
the problem is unary NP-hard.Comment: Subsumes and replaces cs.DS/0412094 and "Complexity of mean flow time
scheduling problems with release dates" by P.B, S.
Scheduling to Minimize Total Weighted Completion Time via Time-Indexed Linear Programming Relaxations
We study approximation algorithms for scheduling problems with the objective
of minimizing total weighted completion time, under identical and related
machine models with job precedence constraints. We give algorithms that improve
upon many previous 15 to 20-year-old state-of-art results. A major theme in
these results is the use of time-indexed linear programming relaxations. These
are natural relaxations for their respective problems, but surprisingly are not
studied in the literature.
We also consider the scheduling problem of minimizing total weighted
completion time on unrelated machines. The recent breakthrough result of
[Bansal-Srinivasan-Svensson, STOC 2016] gave a -approximation for the
problem, based on some lift-and-project SDP relaxation. Our main result is that
a -approximation can also be achieved using a natural and
considerably simpler time-indexed LP relaxation for the problem. We hope this
relaxation can provide new insights into the problem
Stochastic scheduling on unrelated machines
Two important characteristics encountered in many real-world scheduling problems are heterogeneous machines/processors and a certain degree of uncertainty about the actual sizes of jobs. The first characteristic entails machine dependent processing times of jobs and is captured by the classical unrelated machine scheduling model.The second characteristic is adequately addressed by stochastic processing times of jobs as they are studied in classical stochastic scheduling models. While there is an extensive but separate literature for the two scheduling models, we study for the first time a combined model that takes both characteristics into account simultaneously. Here, the processing time of job on machine is governed by random variable , and its actual realization becomes known only upon job completion. With being the given weight of job , we study the classical objective to minimize the expected total weighted completion time , where is the completion time of job . By means of a novel time-indexed linear programming relaxation, we compute in polynomial time a scheduling policy with performance guarantee . Here, is arbitrarily small, and is an upper bound on the squared coefficient of variation of the processing times. We show that the dependence of the performance guarantee on is tight, as we obtain a lower bound for the type of policies that we use. When jobs also have individual release dates , our bound is . Via , currently best known bounds for deterministic scheduling are contained as a special case
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