Scheduling chain-structured tasks to minimize makespan and mean flow time

SUMMARY Performance properties of list scheduling algorithms under various dynamic assumptions are analyzed. The focus is on bounds for scheduling directed acyclic graphs with arbitrary precedence constrains and arbitrary task processing times subject to minimizing the makespan. New performance bounds are derived and compared with known results. key words: list scheduling, worst case analysis, on-line scheduling.

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Section: General Properties Of Schedulesmentioning

confidence: 99%

Worst Case Behavior of List Algorithms for Dynamic Scheduling of Non-unit Execution Time Tasks with Arbitrary Precedence Constrains

Tchernykh

Ecker

2008

IEICE Transactions on Fundamentals of Electronics, Communicatio

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“…We remark that Du, Leung & Young [DLY91] showed P 2|prec|C max to be strongly NP-hard. Whereas, P 2|prec, p j = 1|C max is known to be polynomially solvable by techniques from matching theory (Fujii,Kasami & Ninomiya [FKN69]).…”

Section: Introductionmentioning

confidence: 99%

Conditional hardness of precedence constrained scheduling on identical machines

Svensson

2010

Proceedings of the Forty-Second ACM Symposium on Theory of Computing

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Already in 1966, Graham showed that a simple procedure called list scheduling yields a 2-approximation algorithm for the central problem of scheduling precedence constrained jobs on identical machines to minimize makespan. Till this date it has remained the best algorithm and whether it can or cannot be improved has become a major open problem in scheduling theory.Assuming a new variant of the unique games conjecture (introduced by Bansal & Khot), we resolve this problem by showing that the scheduling problem is NP-hard to approximate within a factor strictly less than 2. The result is obtained by establishing a quite surprising relation between the approximability of the considered problem and that of scheduling precedence constrained jobs on a single machine to minimize weighted completion time. This relation between two classical scheduling problems is interesting on its own. In particular, a tight hardness result for the latter problem implies a tight hardness result for the considered problem.

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“…The related scenarios are studied: scheduling malleable tasks [5], scheduling chainstructured tasks [6], and scheduling with release time constraint [7]. However, they are focus on the complexity analysis, and they cannot directly applied in our multiple phases scenario.…”

Section: Introductionmentioning

confidence: 99%

Performance analysis of work-conserving schedulers for minimizing total flow-time with phase precedence

Zheng

Sinha

Shroff

2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-We consider the problem of minimizing the total flow time of multiple jobs in a pool of multiple homogenous machines, where the jobs arrive over time and have to be served with phase precedence. This is a common occurrence in job scheduling for the increasingly popular data center oriented systems, where jobs need to be processed through a MAP and Reduce procedure before leaving the system. For this problem, one can construct an arrival pattern such that no scheduler can achieve a constant competitive ratio. However, what we find is that by using a slightly weaker metric of performance, which we call the efficiency ratio. We say that a scheduler achieves an efficiency ratio of γ when the flow time incurred by that scheduler divided by the minimum flow time achieved over all possible schedulers is less than or equal to γ almost surely, when the time slots or job arrivals go to infinity. We show a surprising property that any work-conserving scheduler for the flow time problem with phase precedence has a constant efficiency ratio in both preemptive and non-preemptive scenarios under some weak assumptions. We provide numerical results to support our analysis.

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Scheduling chain-structured tasks to minimize makespan and mean flow time

Cited by 87 publications

References 5 publications

Worst Case Behavior of List Algorithms for Dynamic Scheduling of Non-unit Execution Time Tasks with Arbitrary Precedence Constrains

Worst Case Behavior of List Algorithms for Dynamic Scheduling of Non-unit Execution Time Tasks with Arbitrary Precedence Constrains

Conditional hardness of precedence constrained scheduling on identical machines

Performance analysis of work-conserving schedulers for minimizing total flow-time with phase precedence

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