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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2511.03485 |
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| _version_ | 1866914436455858176 |
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| author | Geng, Yutong Sun, Enze Yang, Zonghan Zhang, Yuhao |
| author_facet | Geng, Yutong Sun, Enze Yang, Zonghan Zhang, Yuhao |
| contents | This paper studies the online scheduling problem of minimizing total flow time for $n$ jobs on $m$ identical machines. A classical $Ω(n)$ lower bound shows that no deterministic single-machine algorithm can beat the trivial greedy, even when $n$ is known in advance. However, this barrier is specific to deterministic algorithms on a single machine, leaving open what randomization, multiple machines, or the kill-and-restart capability can achieve.
We give a nearly complete answer. For randomized non-preemptive algorithms, we establish a tight $Θ(\sqrt{n/m})$ competitive ratio, which also improves the best offline approximation to $O(\sqrt{n/m})$. For deterministic non-preemptive algorithms on multiple machines, we prove an $O(n/m^2 + \sqrt{n/m}\log m)$ upper bound and an $Ω(n/m^2 + \sqrt{n/m})$ lower bound. In the kill-and-restart model, we reveal a sharp transition for deterministic algorithms: $Ω(n/\log n)$ for $m = 1$ versus $Θ(\sqrt{n/m})$ for $m \ge 2$; the latter matches the optimal randomized ratio, and we further show that randomization provides no additional power in this model.
We also investigate the setting where $n$ is unknown. We prove that no randomized non-preemptive algorithm achieves $o(n)$ on one machine or $o(n/m^2 + \sqrt{n/m})$ on $m$ machines. In contrast, our kill-and-restart algorithm achieves $O(n^α/\sqrt{m})$ for $m \ge 2$, where $α= (\sqrt{5}-1)/2$, breaking the trivial bound without knowledge of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03485 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Online Flow Time Minimization: Tight Bounds for Non-Preemptive Algorithms Geng, Yutong Sun, Enze Yang, Zonghan Zhang, Yuhao Data Structures and Algorithms This paper studies the online scheduling problem of minimizing total flow time for $n$ jobs on $m$ identical machines. A classical $Ω(n)$ lower bound shows that no deterministic single-machine algorithm can beat the trivial greedy, even when $n$ is known in advance. However, this barrier is specific to deterministic algorithms on a single machine, leaving open what randomization, multiple machines, or the kill-and-restart capability can achieve. We give a nearly complete answer. For randomized non-preemptive algorithms, we establish a tight $Θ(\sqrt{n/m})$ competitive ratio, which also improves the best offline approximation to $O(\sqrt{n/m})$. For deterministic non-preemptive algorithms on multiple machines, we prove an $O(n/m^2 + \sqrt{n/m}\log m)$ upper bound and an $Ω(n/m^2 + \sqrt{n/m})$ lower bound. In the kill-and-restart model, we reveal a sharp transition for deterministic algorithms: $Ω(n/\log n)$ for $m = 1$ versus $Θ(\sqrt{n/m})$ for $m \ge 2$; the latter matches the optimal randomized ratio, and we further show that randomization provides no additional power in this model. We also investigate the setting where $n$ is unknown. We prove that no randomized non-preemptive algorithm achieves $o(n)$ on one machine or $o(n/m^2 + \sqrt{n/m})$ on $m$ machines. In contrast, our kill-and-restart algorithm achieves $O(n^α/\sqrt{m})$ for $m \ge 2$, where $α= (\sqrt{5}-1)/2$, breaking the trivial bound without knowledge of $n$. |
| title | Online Flow Time Minimization: Tight Bounds for Non-Preemptive Algorithms |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2511.03485 |