Distributed Greedy Approximation to Maximum Weighted Independent Set for Scheduling With Fading Channels

Abstract

It has been known that scheduling algorithms designed to achieve throughput optimality and good delay performance often require solving the Maximum Weighted Independent Set (MWIS) problem. However, under most realistic network settings, the MWIS problem is known to be NP-hard. In non-fading environments, low-complexity scheduling algorithms have been provided that converge either to the MWIS solution in time or to a solution that achieves at least a provable fraction of the achievable throughput. However, in more practical systems the channel conditions can vary at faster time-scales than convergence occurs in these lower-complexity algorithms. Hence, these algorithms cannot take advantage of opportunistic gains, and may no longer result in achieving good performance. In this paper, we propose a low-complexity scheduling scheme that performs provably well under fading channels and is amenable to implement in a distributed manner. To the best of our knowledge, this is the first scheduling scheme under fading environments that requires only local information, has a low complexity that grows logarithmically with the network size (provided that the conflict graph has bounded maximum vertex degree), and achieves provable performance guarantees (arbitrarily close to that of the well-known centralized Greedy Maximal Scheduler). We verify that the throughput and the delay of our proposed scheme are close to those of the optimal MaxWeight that solves MWIS at each time. Further, we implement our algorithm in a testbed by modifying the existing IEEE 802.11 DCF. The experiment results show that our implementation successfully accounts for wireless fading, attains the short-term opportunistic gains in practice, and hence substantially outperforms IEEE 802.11 DCF.