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.

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