Efficient link scheduling in a wireless network is challenging. Typical optimal algorithms require solving an NP-hard subproblem. To meet the challenge, one stream of research focuses on finding simpler suboptimal algorithms that have low complexity but high efficiency in practice. In this paper, we study the performance guarantee of one such scheduling algorithm, the longest-queue-first (LQF) algorithm. It is known that the LQF algorithm achieves the full capacity region,$\Lambda $, when the interference graph satisfies the so-called local pooling condition. For a general graph$G$, LQF achieves (i.e., stabilizes) a part of the capacity region,$\sigma ^{\ast }(G) \Lambda $, where$\sigma ^{\ast }(G)$is the overall local pooling factor of the interference graph$G$and$\sigma ^{\ast }(G) \leq 1$. It has been shown later that LQF achieves a larger rate region,$\Sigma ^{\ast }(G) \Lambda $, where$\Sigma ^{\ast }(G)$is a diagonal matrix. The contribution of this paper is to describe three new achievable rate regions, which are larger than the previously known regions. In particular, the new regions include all the extreme points of the capacity region and are not convex in general. We also discover a counterintuitive phenomenon in which increasing the arrival rate may sometime help to stabilize the network. This phenomenon can be well explained using the theory developed in this paper.

One of the major challenges in wireless networking is how to optimize the link scheduling decisions under interference constraints. Recently, a few algorithms have been introduced to address the problem. However, solving the problem to optimality for general wireless interference models is known to be NP-hard. The research community is currently focusing on finding simpler suboptimal scheduling algorithms and on characterizing the algorithm performance. In this paper, we address the performance of a specific scheduling policy called Longest Queue First (LQF), which has gained significant recognition lately due to its simplicity and high efficiency in empirical studies. There has been a sequence of studies characterizing the guaranteed performance of the LQF schedule, culminating at the construction of the σ-local pooling concept by Joo In this paper, we refine the notion of σ -local pooling and use the refinement to capture a larger region of guaranteed performance.

The paper studies the complexity of the wireless scheduling problem under interference constraints. We first relate the definition of the capacity region to the weighted fractional coloring problem. Then, the scheduling-for-stability problem under deterministic arrivals is studied in light of this relationship. We emphasize the requirement that the scheduling algorithm uses a tractable amount of processing and storage resources. Two classes of algorithms are defined and a complexity result is derived for the intersection of the two classes. We also exhibit an algorithm that can achieve the storage requirement by relaxing the processing requirement. The results are used to examine interesting sections of the capacity region. Finally, we relate the new interpretation and theory about the capacity region to the notion of set ¿-local pooling.

One of the major challenges in wireless networking is how to optimize the link scheduling decisions under interference constraints. Recently, a few algorithms have been introduced to address the problem. However, solving the problem to optimality for general wireless interference models is known to be NP-hard. The research community is currently focusing on finding simpler, sub-optimal scheduling algorithms and on characterizing the algorithm performance. In this paper, we address the performance of a specific scheduling policy called Longest Queue First (LQF), which has gained significant recognition lately due to its simplicity and high efficiency in empirical studies. There has been a sequence of studies characterizing the guaranteed performance of the LQF schedule, culminating at the construction of the σ-local pooling concept by Joo et al. [10]. In this paper, we refine the notion of σ-local pooling and use the refinement to capture a larger region of guaranteed performance.