Combinatorial algorithms for minimizing the weighted sum of completion times on a single machine

Davis, James M.; Gandhi, Rajiv; Kothari, Vijay H.

doi:10.1016/j.orl.2012.12.001

Cited by 6 publications

(2 citation statements)

References 21 publications

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“…The primal-dual algorithm (Algorithm 1) is inspired by the work of Davis et al [13] and Ahmadi et al [2]. In this algorithm, a feasible schedule is constructed iteratively from right to left, determining the processing order of coflows, starting from the last coflow and moving towards the first.…”

Section: Approximation Algorithm For the Flow-level Scheduling Problemmentioning

confidence: 99%

Efficient Approximation Algorithms for Scheduling Coflows With Total Weighted Completion Time in Identical Parallel Networks

Chen

2024

IEEE Trans. Cloud Comput.

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This paper addresses the scheduling problem of coflows in identical parallel networks, a well-known N P-hard problem. We consider both flow-level scheduling and coflow-level scheduling problems. In the flow-level scheduling problem, flows within a coflow can be transmitted through different network cores, while in the coflow-level scheduling problem, flows within a coflow must be transmitted through the same network core. The key difference between these two problems lies in their scheduling granularity. Previous approaches relied on linear programming to solve the scheduling order. In this paper, we enhance the efficiency of solving by utilizing the primal-dual method. For the flow-level scheduling problem, we propose an approximation algorithm that achieves approximation ratios of 6 − 2 m and 5 − 2 m for arbitrary and zero release times, respectively, where m represents the number of network cores. Additionally, for the coflow-level scheduling problem, we introduce an approximation algorithm that achieves approximation ratios of 4m + 1 and 4m for arbitrary and zero release times, respectively. The algorithm presented in this paper has practical applications in data centers, such as those operated by Google or Facebook. The simulated results demonstrate the superior performance of our algorithms compared to previous approach, emphasizing their practical utility.

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Section: Approximation Algorithm For the Flow-level Scheduling Problemmentioning

confidence: 99%

Efficient Approximation Algorithms for Scheduling Coflows With Total Weighted Completion Time in Identical Parallel Networks

Chen

2024

IEEE Trans. Cloud Comput.

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“…The primal-dual algorithm, as depicted in Appendix A, Algorithm 3, is inspired by the research of Davis et al [12] and Ahmadi et al [2], respectively. This algorithm constructs a feasible schedule iteratively, progressing from right to left, determining the processing order of coflows.…”

Section: Approximation Algorithm For the Flow-level Scheduling Problemmentioning

confidence: 99%

Efficient Approximation Algorithms for Scheduling Coflows With Precedence Constraints in Identical Parallel Networks to Minimize Weighted Completion Time

Chen

2024

IEEE Trans. Serv. Comput.

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This paper focuses on the problem of coflow scheduling with precedence constraints in identical parallel networks, a well-known N P-hard problem. Coflow is a relatively new network abstraction that characterizes communication patterns in data centers. When considering workload sizes and weights that are dependent on the network topology in the input instances, the proposed algorithm for the flow-level scheduling problem achieves an approximation ratio of O(χ) where χ is the coflow number of the longest path in the directed acyclic graph (DAG). Additionally, when taking into account topology-dependent workload sizes, the algorithm achieves an approximation ratio of O(Rχ), where R represents the ratio of maximum weight to minimum weight. For the coflow-level scheduling problem, the proposed algorithm achieves an approximation ratio of O(mχ), where m is the number of network cores when considering workload sizes and weights that are topology-dependent. Moreover, when considering topology-dependent workload sizes, the algorithm achieves an approximation ratio of O(Rmχ). In the coflows of multi-stage job scheduling problem, the proposed algorithm achieves an approximation ratio of O(χ). Although our theoretical results are based on a limited set of input instances, experimental findings show that the results for general input instances outperform the theoretical results.

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On Scheduling Coflows

Ahmadi

Khuller

Purohit

et al. 2017

Integer Programming and Combinatorial Optimization

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Combinatorial algorithms for minimizing the weighted sum of completion times on a single machine

Cited by 6 publications

References 21 publications

Efficient Approximation Algorithms for Scheduling Coflows With Total Weighted Completion Time in Identical Parallel Networks

Efficient Approximation Algorithms for Scheduling Coflows With Total Weighted Completion Time in Identical Parallel Networks

Efficient Approximation Algorithms for Scheduling Coflows With Precedence Constraints in Identical Parallel Networks to Minimize Weighted Completion Time

On Scheduling Coflows

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