A 3.42-Approximation Algorithm for Scheduling Malleable Tasks under Precedence Constraints

Chen, Chi‐Yeh; Chu, Chih‐Ping

doi:10.1109/tpds.2012.258

Cited by 22 publications

(4 citation statements)

References 19 publications

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“…Offline Scheduling Online Scheduling Independent Tasks Monotonic model : [3,8,26,27,17] Arbitrary model : [29,25,16,17] Comm. model (over time) [15,11,23] Arbitrary model (one-by-one): [33] Task Graphs Roofline model : [31] Monotonic model : [4,19,10,24,20] Roofline model : [31,13] Common models: [5,6,7], [this paper]…”

Section: Related Workmentioning

confidence: 99%

“…When assuming that the area of a job is a concave function of the number of processors, Jansen and Zhang [19] proposed a 3.29-approximation algorithm. Chen and Chu [10] improved the ratio to around 2.95 by further assuming that the execution time of a job is strictly decreasing in the number of allocated processors.…”

Section: Related Workmentioning

confidence: 99%

“…Remarks. We point out that the two bounds shown in Lemma 6, i.e., Inequalities (10) and (11), must be satisfied by all tasks in a task graph for the derived competitive ratio shown in Equation (12) to hold. In Section 4.3, we will prove that, for a given speedup model and regardless of the task parameters, there always exists a processor allocation that satisfies the two bounds with a particular (α, β) choice that achieves the minimum (or close to minimum) competitive ratio.…”

mentioning

confidence: 98%

“…otherwise there would exist an x ≤ 0.1 such that A allocates at least Based on the previous analysis, we now consider s = sup(U) ∈ [0 1,10]…”

mentioning

confidence: 99%

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Online Scheduling of Moldable Task Graphs under Common Speedup Models

Benoît

Perotin

Robert

et al. 2022

Proceedings of the 51st International Conference on Parallel Processing

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

mentioning

confidence: 98%

“…otherwise there would exist an x ≤ 0.1 such that A allocates at least Based on the previous analysis, we now consider s = sup(U) ∈ [0 1,10]…”

mentioning

confidence: 99%

See 2 more Smart Citations

Online Scheduling of Moldable Task Graphs under Common Speedup Models

Benoît

Perotin

Robert

et al. 2022

Proceedings of the 51st International Conference on Parallel Processing

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One step toward bridging the gap between theory and practice in moldable task scheduling with precedence constraints

Hunold

2014

Concurrency and Computation

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Because of the increasing number of cores of current parallel machines and the growing need for a concurrent execution of tasks, the problem of parallel task scheduling is more relevant than ever, especially under the moldable task model, in which tasks are allocated to a fixed number of processors before execution. Much research has been conducted to develop efficient scheduling algorithms for moldable tasks, both in theory and practice. The problem is that theoretical and practical approaches expose shortcomings, for example, many approximation algorithms only guarantee bounds under assumptions, which are unrealistic in practice, or most heuristics have not been rigorously compared with competing approximation algorithms. In particular, it is often assumed that the speedup function of moldable tasks is either non-decreasing, sublinear, or concave. In practice, however, the resulting speedup of parallel programs on current hardware with deep memory hierarchies is most often neither non-decreasing nor concave. We present a new algorithm for the problem of scheduling moldable tasks with precedence constraints for the makespan objective and for arbitrary speedup functions. We show through simulation that the algorithm not only creates competitive schedules for moldable tasks with arbitrary speedup functions but also outperforms other published heuristics and approximation algorithms for non-decreasing speedup functions.We have conducted three different simulation studies, which are part of the overall evaluation. First, we compare the schedules produced by CPA13 and its competitors for the non-increasing and convex run-time model. Second, we address the scalability of these algorithms by increasing the number

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Handling precedence constraints in scheduling problems by the sequence pair representation

Kozik

2015

J Comb Optim

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In this paper, we show that sequence pair (SP) representation, primarily applied to the rectangle packing problems appearing in the VLSI industry, can be a solution representation of precedence constrained scheduling. We present three interpretations of sequence pair, which differ in complexity of schedule evaluation and size of a corresponding solution space. For each interpretation we construct an incremental precedence constrained SP neighborhood evaluation algorithm, computing feasibility of each solution in the insert neighborhood in an amortized constant time per examined solution, and prove the connectivity property of the considered neighborhoods. To compare proposed interpretations of SP, we construct heuristic and metaheuristic algorithms for the multiprocessor job scheduling problem, and verify their efficiency in the numerical experiment.

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A 3.42-Approximation Algorithm for Scheduling Malleable Tasks under Precedence Constraints

Cited by 22 publications

References 19 publications

Online Scheduling of Moldable Task Graphs under Common Speedup Models

Online Scheduling of Moldable Task Graphs under Common Speedup Models

One step toward bridging the gap between theory and practice in moldable task scheduling with precedence constraints

Handling precedence constraints in scheduling problems by the sequence pair representation

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