¹Provincial Key Laboratory for High-Performance Computing Technology, Jiangxi Normal University, Nanchang, 330022, China
²State Key Laboratory of Software Engineering, Wuhan University, Wuhan, 430072, China

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Abstract—Distribution and dynamics are the main characteristics of resource allocation problem. Despite the variety of approaches and models proposed for the problem, a systematic formalization and a general solution strategy are missing. This paper takes a step towards this goal by proposing a categorical formalization of resource allocation, which not only represents both distributed and dynamic features, but also formally prove the properties of symmetry, safety(non-deadlock), liveness(non-starvation) and concurrency. The application to the wireless sensor networks demonstrates the practicability of our formal model and emphasizes the strengths of category theory – its simple theory, abstract mechanism, diagrammatical representation and its expressive power in representing and reasoning many concepts of computer science.

Index Terms—Resource Allocation, Category Theory, Formal Model, Wireless Sensor Networks.

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Cite: Zhen Youa, Jinyun Xuea, Ying Shi, Dongming Jiang, Qimin Hu, "Formalization of Distributed and Dynamic Resources Allocation Using Category Theory," Journal of Software vol. 8, no. 12, pp. 3088-3095, 2013.