Graph jobs represent a wide variety of computation-intensive tasks in which computations are represented by graphs consisting of components (denoting either data sources or data processing) and edges (corresponding to data flows between the components). Recent years have witnessed dramatic growth in smart vehicles and computation-intensive graph jobs, which pose new challenges to the provision of efficient services related to the Internet of Vehicles. Fortunately, vehicular clouds formed by a collection of vehicles, which allows jobs to be offloaded among vehicles, can substantially alleviate heavy on-board workloads and enable on-demand provisioning of computational resources. In this paper, we present a novel framework for vehicular clouds that maps components of graph jobs to service providers via opportunistic vehicle-to-vehicle communication. Then, graph job allocation over vehicular clouds is formulated as a non-linear integer programming with respect to vehicles contact duration and available resources, aiming to minimize job completion time and data exchange cost. The problem is addressed for two scenarios: low-traffic and rush-hours. For the former, we determine the optimal solutions for the problem. In the latter case, given the intractable computations for deriving feasible allocations, we propose a novel low complexity randomized graph job allocation mechanism by considering hierarchical tree based subgraph isomorphism. We evaluate the performance of our proposed algorithms through extensive simulations.
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