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We design a parallel algorithm for the Constrained Shortest Path (CSP) problem. The CSP problem is known to be NP-hard and there exists a pseudo-polynomial time sequential algorithm that solves it. To design the parallel algorithm, we extend the techniques used in the design of the Δ-stepping algorithm for the single-source shortest paths problem. 

In Vehicular Edge Computing (VEC) systems, the computing resources of connected Electric Vehicles (EV) are used to fulfill the low-latency computation requirements of vehicles. However, local execution of heavy workloads may drain a considerable amount of energy in EVs. One promising way to improve the energy efficiency is to share and coordinate computing resources among connected EVs. However, the uncertainties in the future location of vehicles make it hard to decide which vehicles participate in resource sharing and how long they share their resources so that all participants benefit from resource sharing. In this paper, we propose VECMAN, a framework for energy-aware resource management in VEC systems composed of two algorithms: (i) a resource selector algorithm that determines the participating vehicles and the duration of resource sharing period; and (ii) an energy manager algorithm that manages computing resources of the participating vehicles with the aim of minimizing the computational energy consumption. We evaluate the proposed algorithms and show that they considerably reduce the vehicles computational energy consumption compared to the state-of-the-art baselines. Specifically, our algorithms achieve between 7% and 18% energy savings compared to a baseline that executes workload locally and an average of 13% energy savings compared to a baseline that offloads vehicles workloads to RSUs. 

In this paper, we address the Multi-Component Application Placement Problem (MCAPP) in Mobile Edge Computing (MEC) systems. We formulate this problem as a Mixed Integer Non-Linear Program (MINLP) with the objective of minimizing the total cost of running the applications. In our formulation, we take into account two important and challenging characteristics of MEC systems, the mobility of users and the network capabilities. We analyze the complexity of MCAPP and prove that it is NP-hard, that is, finding the optimal solution in reasonable amount of time is infeasible. We design two algorithms, one based on matching and local search and one based on a greedy approach, and evaluate their performance by conducting an extensive experimental analysis driven by two types of user mobility models, real-life mobility traces and random-walk. The results show that the proposed algorithms obtain near-optimal solutions and require small execution times for reasonably large problem instances. 

In this paper, we address the problem of application placement in MEC systems that takes into account the risk of exceeding the energy budget of the edge servers. We formulate the problem as a chance-constrained program, where the objective is to maximize the total quality of service in the system, while keeping the expected risk of exceeding the edge servers' energy budget within an acceptable threshold. We develop a learning-based method to solve the problem which requires a very small execution time for large size instances. We evaluate the performance of the proposed method by conducting an extensive experimental analysis. 

The low-latency requirements of connected electric vehicles and their increasing computing needs have led to the necessity to move computational nodes from the cloud data centers to edge nodes such as road-side units (RSU). However, offloading the workload of all the vehicles to RSUs may not scale well to an increasing number of vehicles and workloads. To solve this problem, computing nodes can be installed directly on the smart vehicles, so that each vehicle can execute the heavy workload locally, thus forming a vehicular edge computing system. On the other hand, these computational nodes may drain a considerable amount of energy in electric vehicles. It is therefore important to manage the resources of connected electric vehicles to minimize their energy consumption. In this paper, we propose an algorithm that manages the computing nodes of connected electric vehicles for minimized energy consumption. The algorithm achieves energy savings for connected electric vehicles by exploiting the discrete settings of computational power for various performance levels. We evaluate the proposed algorithm and show that it considerably reduces the vehicles' computational energy consumption compared to state-of-the-art baselines. Specifically, our algorithm achieves 15-85% energy savings compared to a baseline that executes workload locally and an average of 51% energy savings compared to a baseline that offloads vehicles' workloads only to RSUs.