The explosive growth of short video platforms has generated a massive surge in global traffic, imposing heavy financial burdens on content providers. While Peer-to-Peer Content Delivery Networks (PCDNs) offer a cost-effective alternative by leveraging resource-constrained edge nodes, the limited storage and concurrent service capacities of these peers struggle to absorb the intense temporal demand spikes characteristic of short video consumption. In this paper, we propose to minimize transmission costs by exploiting a novel degree of freedom, the inherent flexibility of server-driven playback sequences. We formulate the Optimal Video Ordering and Transmission Scheduling (OVOTS) problem as an Integer Linear Program to jointly optimize personalized video ordering and transmission scheduling. By strategically permuting playlists, our approach proactively smooths temporal traffic peaks, maximizing the offloading of requests to low-cost peer nodes. To solve the OVOTS problem, we provide a rigorous theoretical reduction of the OVOTS problem to an auxiliary Minimum Cost Maximum Flow (MCMF) formulation. Leveraging König's Edge Coloring Theorem, we prove the strict equivalence of these formulations and develop the Minimum-cost Maximum-flow with Edge Coloring (MMEC) algorithm, a globally optimal, polynomial-time solution. Extensive simulations demonstrate that MMEC significantly outperforms baseline strategies, achieving cost reductions of up to 67% compared to random scheduling and 36% compared to a simulated annealing approach. Our results establish playback sequence flexibility as a robust and highly effective paradigm for cost optimization in PCDN architectures.

翻译：短视频平台的爆炸式增长引发了全球流量的急剧攀升，给内容提供商带来了沉重的财务负担。虽然对等内容分发网络通过利用资源受限的边缘节点提供了一种经济高效的替代方案，但这些对等节点有限的存储和并发服务能力难以应对短视频消费所特有的瞬时需求高峰。本文提出通过利用一种新颖的自由度——服务器驱动播放序列的固有灵活性——来最小化传输成本。我们将最优视频排序与传输调度问题建模为一个整数线性规划，以联合优化个性化视频排序和传输调度。通过策略性地调整播放列表顺序，我们的方法能够主动平滑瞬时流量峰值，最大限度地将来请求卸载至低成本的对等节点。为解决OVOTS问题，我们提供了从OVOTS问题到辅助的最小费用最大流问题的严格理论归约。利用柯尼希边着色定理，我们证明了这两种表述的严格等价性，并开发了基于边着色的最小费用最大流算法——一种全局最优的多项式时间求解方法。大量仿真实验表明，MMEC算法显著优于基线策略，与随机调度相比可实现高达67%的成本降低，与模拟退火方法相比可降低36%。我们的研究结果确立了播放序列灵活性作为PCDN架构中一种稳健且高效的成本优化范式。