发表机构
Institut Polytechnique de Paris; Huawei Technologies Ltd.; Université Clermont Auvergne（巴黎理工学院; 华为技术有限公司; 克莱蒙奥弗涅大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对实时服务的延迟保障需求，研究强NP难的延迟约束最大并发流问题，提出基于二阶锥约束的凸松弛方法及多项式时间近似算法，通过实验验证其性能优于现有方法。
AI 中文摘要
VoIP、大规模神经网络训练等实时服务需要严格的传输延迟保障。尽管跳数约束下的路由问题易于处理，但实际延迟会随设备负载急剧增加，通常采用M/M/1排队函数建模，其中延迟与可用带宽成反比。我们研究由此产生的延迟约束下的最大并发流（DCMCF）问题，该问题旨在最大化所有流的最小吞吐量。该问题的复杂性源于延迟约束的条件性和非线性，这些约束仅在流使用的特定路径上生效。我们证明，即使对于单源单目的地实例，DCMCF也是强NP难的。为解决该问题固有的非凸性，我们引入一种新的凸松弛，通过二阶锥约束表示，该约束由表示给定路径上单条弧相关条件延迟的函数的凸包获得。该松弛被证明优于基于析取规划的现有公式。利用这一结果，我们开发了一种具有可证性能保证的多项式时间近似算法，并给出数值实验证明所提方法的有效性。
英文摘要
Real-time services, such as VoIP and large-scale neural network training, require strict transmission delay guarantees. While routing under hop constraints is tractable, real-world delays increase sharply with equipment load, typically modeled using the M/M/1 queuing function where delay is inversely proportional to available bandwidth. We investigate the resulting Delay-Constrained Maximum Concurrent Flow (DCMCF) problem, which seeks to maximize the minimum throughput across all commodities. The problem's complexity stems from the conditional and non-linear nature of the delay constraints, which are active only along the specific paths used by the flow. We prove that DCMCF is strongly NP-hard, even for single-source/single-destination instances. To address the inherent non-convexity of the problem, we introduce a new convex relaxation expressed through second-order cone constraints, obtained from the convex envelope of a function representing the conditional delay associated with a single arc of a given path. The relaxation is shown to outperform existing formulations based on disjunctive programming. Leveraging this result, we develop a polynomial-time approximation algorithm with a provable performance guarantee and present numerical experiments demonstrating the effectiveness of the proposed approach.
