arXiv:2611.09205v1 Announce Type: new Abstract: In this paper, we propose an aerial-marine integrated network architecture tailored for maritime search and rescue (MSAR) operations, where a high altitude platform station (HAPS) and maritime autonomous surface ships (MASSs) are equipped with edge servers, providing computing services for surveillance uncrewed aerial vehicles (UAVs). These UAVs generate substantial volumes of computation-intensive and delay sensitive tasks, some of which can be strategically offloaded to both MASSs and HAPSs for distributed processing. We formulate the joint task offloading and resource allocation as a mixed-integer nonlinear program (MINLP) to minimize the system computation overhead (CO), quantified by a weighted sum of task completion time and energy consumption. Given the stochastic nature of task arrivals from UAVs and the dynamic characteristics of marine channel conditions, we employ a two-stage optimization to decompose the problem into four tractable subproblems, i.e., 1) edge server selection, 2) transmission power allocation, 3) edge computing resource allocation, and 4) local computation resource allocation. In stage I, we optimize the edge server selection via many-to-one matching. In stage II, we determine the transmission power of each UAV with quasi-convex optimization and solve the edge computing and local computing resource allocation subproblems via a projected gradient descent method and convex optimization, respectively. Simulation results validate that the proposed scheme can achieve superior system performance over benchmark schemes.