The Internet of Things promises to enable a wide range of new applications involving sensors, embedded devices and mobile devices. Different from traditional cloud computing, where the centralized and powerful servers offer high quality computing service, in the era of the Internet of Things, there are abundant computational resources distributed over the network. These devices are not as powerful as servers, but are easier to access with faster setup and short-range communication. However, because of energy, computation, and bandwidth constraints on smart things and other edge devices, it will be imperative to collaboratively run a computational-intensive application that a single device cannot support individually. As many IoT applications, like data processing, can be divided into multiple tasks, we study the problem of assigning such tasks to multiple devices taking into account their abilities and the costs, and latencies associated with both task computation and data communication over the network.;A system that leverages collaborative computing over the network faces highly variant run-time environment. For example, the resource released by a device may suddenly decrease due to the change of states on local processes, or the channel quality may degrade due to mobility. Hence, such a system has to learn the available resources, be aware of changes and flexibly adapt task assignment strategy that efficiently makes use of these resources.;We take a step by step approach to achieve these goals. First, we assume that the amount of resources are deterministic and known. We formulate a task assignment problem that aims to minimize the application latency (system response time) subject to a single cost constraint so that we will not overuse the available resource. Second, we consider that each device has its own cost budget and our new multi-constrained formulation clearly attributes the cost to each device separately. Moving a step further, we assume that the amount of resources are stochastic processes with known distributions, and solve a stochastic optimization with a strong QoS constraint. That is, instead of providing a guarantee on the average latency, our task assignment strategy gives a guarantee that p% of time the latency is less than t, where p and t are arbitrary numbers. Finally, we assume that the amount of run-time resources are unknown and stochastic, and design online algorithms that learn the unknown information within limited amount of time and make competitive task assignment.;We aim to develop algorithms that efficiently make decisions at run-time. That is, the computational complexity should be as light as possible so that running the algorithm does not incur considerable overhead. For optimizations based on known resource profile, we show these problems are NP-hard and propose polynomial-time approximation algorithms with performance guarantee, where the performance loss caused by sub-optimal strategy is bounded. For online learning formulations, we propose light algorithms for both stationary environment and non-stationary environment and show their competitiveness by comparing the performance with the optimal offline policy (solved by assuming the resource profile is known).;We perform comprehensive numerical evaluations, including simulations based on trace data measured at application run-time, and validate our analysis on algorithm's complexity and performance based on the numerical results. Especially, we compare our algorithms with the existing heuristics and show that in some cases the performance loss given by the heuristic is considerable due to the sub-optimal strategy. Hence, we conclude that to efficiently leverage the distributed computational resource over the network, it is essential to formulate a sophisticated optimization problem that well captures the practical scenarios, and provide an algorithm that is light in complexity and suggests a good assignment strategy with performance guarantee.
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