In the context of 6G ubiquitous connectivity, the space-air-ground-sea integrated network (SAGSIN) emerges as a new paradigm for pervasive service provisioning. To support expanding maritime activities in infrastructure-scarce ocean areas, we propose an innovative dynamic task and resource scheduling approach for SAGSIN to deliver computing services for vessels. It integrates broad-coverage satellites, relay-capable high-altitude platform (HAP), energy-sufficient coastal base station (BS), and flexibly deployed uncrewed aerial vehicles (UAVs) to accommodate wide-area, highly mobile, and sustained maritime services. To address the challenge of task scheduling across four layers, a dynamic task offloading algorithm is developed. It steers task flows toward servers with light loads, strong computing capabilities, and high-rate links based on real-time system states to reduce task execution delay, integrating an anticipatory satellite handover strategy to mitigate post-handover congestion and improving satellite resource utilization. Considering the limited endurance of UAVs, we impose residual energy constraints to ensure task backlog handover and safe return. Furthermore, the UAV-BS bandwidth allocation, UAV trajectories, and computing resource allocation are jointly optimized to enhance the connectivity among low-altitude devices and accelerate task completion. Simulation results validate the proposed method's superior adaptability to system resource variations during task execution in complex maritime environments, achieving at least a 23% reduction in average task delay over benchmarks.

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