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Non-clairvoyant Weighted Flow Time Scheduling on Different Multi-processor Models

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Abstract

We study non-clairvoyant scheduling to minimize weighted flow time on two different multi-processor models. In the first model, processors are all identical and jobs can possibly be speeded up by running on several processors in parallel. Under the non-clairvoyant model, the online scheduler has no information about the actual job size and degree of speed-up due to parallelism, yet it has to determine dynamically when and how many processors to run the jobs. The literature contains several O(1)-competitive algorithms for this problem under the unit-weight multi-processor setting (Edmonds, Theor. Comput. Sci. 235(1), 109–141, 2000; Edmonds and Pruhs, in Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA), 685–692, 2009) as well as the weighted single-processor setting (Bansal and Dhamdhere, ACM Trans. Algorithms 3(4), 2007). This paper shows the first O(1)-competitive algorithm for weighted flow time in the multi-processor setting.

In the second model, we consider processors with different functionalities and only processors of the same functionality can work on the same job in parallel. Here a job is modeled as a sequence of non-clairvoyant demands of different functionalities. This model is derived naturally from the classical job shop scheduling; but as far as we know, there is no previous work on scheduling to minimize flow time. In this paper we take a first step to study non-clairvoyant scheduling on this multi-processor model. Motivated by the literature on 2-machine job shop scheduling, we focus on the special case when processors are divided into two types of functionalities, and we show a non-clairvoyant algorithm that is O(1)-competitive for weighted flow time.

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Notes

  1. That is, for each time T where such events occur, \(\lim_{t\to T^{-}} \varPhi(t) \ge \lim_{t\to T^{+}} \varPhi(t)\). It should be emphasized that Φ(t) could be discontinuous at T.

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Authors and Affiliations

  1. University of Hong Kong, Pokfulam, Hong Kong

    Jianqiao Zhu, Ho-Leung Chan & Tak-Wah Lam

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  1. Jianqiao Zhu
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  2. Ho-Leung Chan
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  3. Tak-Wah Lam
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Correspondence to Jianqiao Zhu.

Additional information

Ho-Leung Chan is supported in part by GRF Grant HKU 710210E. Tak-Wah Lam is supported in part by HKU Grant 201109176197. A preliminary version of this paper appeared in the 9th Workshop on Approximation and Online Algorithms (WAOA) 2011.

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Zhu, J., Chan, HL. & Lam, TW. Non-clairvoyant Weighted Flow Time Scheduling on Different Multi-processor Models. Theory Comput Syst 56, 82–95 (2015). https://doi.org/10.1007/s00224-013-9475-y

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