Average-Case Analysis of Greedy Matching for D2D Resource Sharing

TL;DR

This paper provides a rigorous average-case analysis of a greedy matching algorithm for D2D resource sharing, showing it performs close to optimal in typical network models with practical implications.

Contribution

It introduces a new asymptotic methodology for analyzing greedy algorithms on random graphs and offers the first average-case performance bounds for D2D sharing networks.

Findings

Greedy algorithm performs over 84.9% of optimal on 2D grid graphs.

Achieves at least 79% of optimal on Erdos-Renyi graphs.

Realistic data shows models closely match practical D2D networks.

Abstract

Given the proximity of many wireless users and their diversity in consuming local resources (e.g., data-plans, computation and even energy resources), device-to-device (D2D) resource sharing is a promising approach towards realizing a sharing economy. In the resulting networked economy, $n$ users segment themselves into sellers and buyers that need to be efficiently matched locally. This paper adopts an easy-to-implement greedy matching algorithm with distributed fashion and only sub-linear $O(\log n)$ parallel complexity, which offers a great advantage compared to the optimal but computational-expensive centralized matching. But is it efficient compared to the optimal matching? Extensive simulations indicate that in a large number of practical cases the average loss is no more than $10\%$, a far better result than the $50\%$ loss bound in the worst case. However, there is no rigorous average-case analysis in the literature to back up such encouraging findings, which is a fundamental step towards supporting the practical use of greedy matching in D2D sharing. This paper is the first to present the rigorous average analysis of certain representative classes of graphs with random parameters, by proposing a new asymptotic methodology. For typical 2D grids with random matching weights we rigorously prove that our greedy algorithm performs better than $84.9\%$ of the optimal, while for typical Erdos-Renyi random graphs we prove a lower bound of $79\%$ when the graph is neither dense nor sparse. Finally, we use realistic data to show that our random graph models approximate well D2D sharing networks encountered in practice.