The software defined air-ground integrated vehicular (SD-AGV) networks have emerged as a promising paradigm, which realize the flexible on-ground resource sharing to support innovative applications for UAVs with heavy computational overhead. In this paper, we investigate a vehicular cloud-assisted graph job allocation problem in SD-AGV networks, where the computation-intensive jobs carried by UAVs, and the vehicular cloud are modeled as graphs. To map each component of the graph jobs to a feasible vehicle, while achieving the trade-off among minimizing UAVs job completion time, energy consumption, and the data exchange cost among vehicles, we formulate the problem as a mixed-integer non-linear programming problem, which is Np-hard. Moreover, the constraint associated with preserving job structures poses addressing the subgraph isomorphism problem, that further complicates the algorithm design. Motivated by which, we propose an efficient decoupled approach by separating the template (feasible mappings between components and vehicles) searching from the transmission power allocation. For the former, we present an efficient algorithm of searching for all the subgraph isomorphisms with low computation complexity. For the latter, we introduce a power allocation algorithm by applying convex optimization techniques. Extensive simulations demonstrate that the proposed approach outperforms the benchmark methods considering various problem sizes.
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