Average-Case Analysis of Greedy Matching for Large-Scale D2D Resource Sharing

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 $O(\log n)$O(logn) parallel complexity (in user number $n$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.