Given the proximity of many wireless users and their diversity in consuming local resources (e.g., data-plans, computation and energy resources), device-to-device (D2D) resource sharing is a promising approach towards realizing a sharing economy. This paper adopts an easy-to-implement greedy matching algorithm with distributed fashion and only sub-linear O(log n) parallel complexity (in user number n) for large-scale D2D sharing. Practical cases indicate that the greedy matching's average performance is far better than the worst-case approximation ratio 50% as compared to the optimum. However, there is no rigorous average-case analysis in the literature to back up such encouraging findings and this paper is the first to present such analysis for multiple representative classes of graphs. For 1D linear networks, we prove that our greedy algorithm performs better than 86.5% of the optimum. For 2D grids, though dynamic programming cannot be directly applied, we still prove this average performance ratio to be above 76%. For the more challenging Erdos-Renyi random graphs, we equivalently reduce to the asymptotic analysis of random trees and successfully prove a ratio up to 79%. Finally, we conduct experiments using real data to simulate realistic D2D networks, and show that our analytical performance measure approximates well practical cases.

翻译：鉴于众多无线用户的空间邻近性及其在本地资源（如数据套餐、计算与能源资源）消费上的多样性，设备到设备（D2D）资源共享是实现共享经济的一种有前景的方法。本文采用一种易于实现的分布式贪心匹配算法，其并行复杂度（关于用户数量n）仅为次线性O(log n)，适用于大规模D2D共享。实际案例表明，与最优解相比，贪心匹配的平均性能远优于最坏情况下的50%近似比。然而，现有文献中缺乏严格的平均情况分析来支持这一积极发现，本文首次针对多个代表性图类进行了此类分析。对于一维线性网络，我们证明贪心算法的性能优于最优解的86.5%。对于二维网格，尽管动态规划无法直接应用，我们仍证明其平均性能比超过76%。对于更具挑战性的Erdos-Renyi随机图，我们将其等价简化为随机树的渐近分析，并成功证明近似比可达79%。最后，我们利用真实数据模拟实际D2D网络进行实验，表明我们的分析性能度量能够很好地近似实际场景。