Greedy maximal matching: Performance limits for arbitrary network graphs under the node-exclusive interference model

Greedy Maximal Matching (GMM) is an important scheduling scheme for multi-hop wireless networks. It is computationally simple, and has often been numerically shown to achieve throughput that is close to optimal. However, to date the performance limits of GMM have not been well understood. In particular, although a lower bound on its performance has been well known, this bound has been empirically found to be quite loose. In this paper, we focus on the well-established node-exclusive interference model and provide new analytical results that characterize the performance of GMM through a topological notion called the local-pooling factor. We show that for a given network graph with single-hop traffic, the efficiency ratio of GMM (i.e., the worst-case ratio of the throughput of GMM to that of the optimal) is equal to its local-pooling factor. Further, we estimate the local-pooling factor for arbitrary network graphs under the node-exclusive interference model and show that the efficiency ratio of GMM is no smaller than d* /2d* - 1 in a network topology of maximum node-degree d*. Using these results, we identify specific network topologies for which the efficiency ratio of GMM is strictly less than 1. We also extend the results to the more general scenario with multi-hop traffic, and show that GMM can achieve similar efficiency ratios when a flow-regulator is used at each hop.