Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing

Henning, Sören; Jansen, Klaus; Rau, Malin; Schmarje, Lars

doi:10.1007/978-3-319-90530-3_15

Cited by 11 publications

(11 citation statements)

References 27 publications

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“…Henning et al [34] study task scheduling in the parallel method challenge with a fixed number of processors and the best schedule for high performance outcomes. They indicate that this can be achieved by mapping tasks to machines according to precedence constraints.…”

Section: ) Related Workmentioning

confidence: 99%

A Task Scheduling Algorithm With Improved Makespan Based on Prediction of Tasks Computation Time algorithm for Cloud Computing

et al. 2019

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Cloud computing is extensively used in a variety of applications and domains, however task and resource scheduling remains an area that requires improvement. Put simply, in a heterogeneous computing system, task scheduling algorithms, which allow the transfer of incoming tasks to machines, are needed to satisfy high performance data mapping requirements. The appropriate mapping between resources and tasks reduces makespan and maximises resource utilisation. In this contribution, we present a novel scheduling algorithm using Directed Acyclic Graph (DAG) based on the Prediction of Tasks Computation Time algorithm (PTCT) to estimate the preeminent scheduling algorithm for prominent cloud data. In addition, the proposed algorithm provides a significant improvement with respect to the makespan and reduces the computation and complexity via employing Principle Components Analysis (PCA) and reducing the Expected Time to Compute (ETC) matrix. Simulation results confirm the superior performance of the algorithm for heterogeneous systems in terms of efficiency, speedup and schedule length ratio, when compared to the state-of-the-art Min-Min, Max-Min, QoS-Guide and MiM-MaM scheduling algorithms. INDEX TERMS Scheduling algorithm, task scheduling, resource utilization, cloud computing. I. INTRODUCTION A. MOTIVATION AND AIM Cloud computing has grown to be a major technological enabler in companies and organizations [1]-[3]. It has been shown to increase reliability, deliver cost-cutting solutions, and provide 24/7/365 access to hard/soft resources from anywhere based on pay/use pricing policy [4], [5]. The cloud offers services in the structure of Software as a Service (SaaS), Infrastructure as a Service (IaaS), and Platform as a Service (PaaS) [3]. Task scheduling is a major challenge in widely distributed heterogeneous systems (e.g., cloud computing), which chooses the preeminent resources for a provided task. Also, in heterogeneous systems, task scheduling is more convoluted in comparison to homogeneous The associate editor coordinating the review of this manuscript and approving it for publication was Yaser Jararweh.

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Section: ) Related Workmentioning

confidence: 99%

A Task Scheduling Algorithm With Improved Makespan Based on Prediction of Tasks Computation Time algorithm for Cloud Computing

et al. 2019

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“…It has an additive term of O(h max /ε 2 ), where h max is the largest occurring item height. The additive term was improved by Sviridenko [30] and Bougeret et al [5] 1 + ε [1] 12/11 [12], 5/4 + ε 5/4, Theorem 1 [8,16] 4/3 + ε [25] 7/5 + ε [18] 3/2 + ε Figure 1: The upper and lower bounds for pseudo-polynomial approximations achieved so far.…”

Section: Related Workmentioning

confidence: 99%

“…Adamaszek, Kociumaka, Pilipczuk, and Pilipczuk [1] proved a lower bound of 12/11 if P = N P . This lower bound was improved to 5/4 by Henning, Jansen, Rau, and Schmarje [12] if P = NP. There are differences in the size of the optimal solutions of the same instances for contiguous task scheduling and the closely related non-contiguous task scheduling P |size j |C max .…”

Section: Related Workmentioning

confidence: 99%

“…In this paper, we study pseudo-polynomial approximation algorithms with respect to the width of the strip, i.e., we consider algorithms where the width of the strip W is allowed to appear polynomially in the running time. Recently, we were able to show that we cannot find an algorithm with approximation ratio strictly better than 5/4 unless P = NP [12]. On the other hand, the algorithm with the best ratio so far computes a 4/3 + ε approximation [8,16].…”

Section: Introductionmentioning

confidence: 99%

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Closing the gap for pseudo-polynomial strip packing

Jansen¹,

Rau²

2017

Preprint

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The set of 2-dimensional packing problems builds an important class of optimization problems and Strip Packing together with 2-dimensional Bin Packing and 2-dimensional Knapsack is one of the most famous of these problems. Given a set of rectangular axis parallel items and a strip with bounded width and infinite height the objective is to find a packing of the items into the strip which minimizes the packing height. We speak of pseudo-polynomial Strip Packing if we consider algorithms with pseudo-polynomial running time with respect to the width of the strip.It is known that there is no pseudo-polynomial algorithm for Strip Packing with a ratio better than 5/4 unless P = NP. The best algorithm so far has a ratio of 4/3 + ε. In this paper, we close this gap between inapproximability result and best known algorithm by presenting an algorithm with approximation ratio 5/4 + ε and thus categorize the problem accurately. The algorithm uses a structural result which states that each optimal solution can be transformed such that it has one of a polynomial number of different forms. The strength of this structural result is that it applies to other problem settings as well for example to Strip Packing with rotations (90 degrees) and Contiguous Moldable Task Scheduling. This fact enabled us to present algorithms with approximation ratio 5/4 + ε for these problems as well.

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“…Предложенные для многопроцессорных вычислительных систем модели горизонтальной полосы с ограниченным, критическим процессорным ресурсом и неограниченным временным ресурсом [6][7][8][9][10][11] заменяются вследствие экспоненциального роста числа процессоров и пропускной мощности каналов связи моделью ресурсного квадранта с паритетной, равновеликой ценностью процессорного и временного ресурсов [12][13][14][15][16].…”

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Dispatching of Circular-Type Applications by the Initial-Ring and Sequential Approximation Algorithm in Grid-Systems

Курейчик¹

2021

News of KBSC RAS

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Аннотация. В статье рассматриваются и исследуются полиномиально трудоёмкие начальнокольцевой и алгоритм последовательных приближений для решения вопроса о практической целесообразности их применения в Grid-системах при обработке массива заявок кругового типа. Моделью Grid-системы с централизованной архитектурой служит первый координатный квадрант, а модель заявки представляется ресурсным прямоугольником. Качество рассматриваемых алгоритмов оценивается неэвклидовой эвристической мерой. В основе предлагаемых алгоритмов лежат операции динамического интегрирования по горизонтали и вертикали с локальным оптимумом. Предложенные алгоритмы анализируются на тестовых массивах, полученных из облицовки квадрата полосами меньших квадратов. Вычисляются эвристические меры ресурсных оболочек начально-кольцевого и алгоритма последовательных приближений, не превосходящие значения 0,61, определяется величина погрешности относительно оптимального значения, не превышающая 22%. Дается рекомендация использовать эти алгоритмы для диспетчирования массивами заявок кругового типа в Grid-системах централизованной архитектуры.

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Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing

Cited by 11 publications

References 27 publications

A Task Scheduling Algorithm With Improved Makespan Based on Prediction of Tasks Computation Time algorithm for Cloud Computing

A Task Scheduling Algorithm With Improved Makespan Based on Prediction of Tasks Computation Time algorithm for Cloud Computing

Closing the gap for pseudo-polynomial strip packing

Dispatching of Circular-Type Applications by the Initial-Ring and Sequential Approximation Algorithm in Grid-Systems

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