The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the impact of the algorithm parameters on the convergence times of the method is still lacking. In this paper we find the optimal algorithm parameters that minimize the convergence factor of the ADMM iterates in the context of l2-regularized minimization and constrained quadratic programming. Numerical examples show that our parameter selection rules significantly outperform existing alternatives in the literature.

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function, we determine the algorithm parameters that guarantee the fastest convergence and characterize situations when signi?cant speed-ups can be obtained over the standard gradient method. Furthermore, we quantify how the performance of the gradient method and its accelerated counterpart are affected by uncertainty in the problem data, and conclude that in most cases our proposed method outperforms gradient descent. Finally, we apply the proposed technique to three engineering problems: resource allocation under network-wide budget constraints, distributed averaging, and Internet congestion control. In all cases, we demonstrate that our algorithm converges more rapidly than alternative algorithms reported in the literature.

Opportunistic routing is widely known to have substantially better performance than unicast routing in wireless networks with lossy links. However, wireless sensor networks are heavily duty-cycled, i.e. they frequently enter sleep states to ensure long network life-time. This renders existing opportunistic routing schemes impractical, as they assume that nodes are always awake and can overhear other transmissions. In this paper we introduce ORW, a practical opportunistic routing scheme for wireless sensor networks. ORW uses a novel opportunistic routing metric, EDC, that reflects the expected number of duty-cycled wakeups that are required to successfully deliver a packet from source to destination. We devise distributed algorithms that find the EDC-optimal forwarding and demonstrate using analytical performance models and simulations that EDC-based opportunistic routing results in significantly reduced delay and improved energy efficiency compared to the traditional unicast routing. We compare the performance of the ORW protocol with other alternatives in both simulations and testbed-based experiments. Our results show that ORW reduces radio duty cycles on average by 50% (up to 90% on individual nodes) and delays by 30% to 90% when compared to the state of the art.

Achieving low-power operation in wireless sensor networks with high data load or bursty traffic is challenging. The hidden terminal problem is aggravated with increased amounts of data in which traditional backoff-based contention resolution mechanisms fail or induce high latency and energy costs. We analyze and optimize Strawman, a receiver-initiated contention resolution mechanism that copes with hidden terminals. We propose new techniques to boost the performance of Strawman while keeping the resolution overhead small. We finally validate our improved mechanism via experiments.

Several analytical models of different wireless networking schemes such as wireless LANs and meshes have been reported in the literature. To the best of our knowledge, all these models fail to address the accurate end-to-end delay analysis of multi-hop wireless networks under unsaturated traffic condition considering the hidden and exposed terminal situation. In an effort to gain deep understanding of delay, this paper firstly proposes a new analytical model to predict accurate media access delay by obtaining its distribution function in a single wireless node. The interesting point of having the media access delay distribution is its generality that not only enables us to derive the average delay which has been reported in almost most of the previous studies as a special case but also facilitates obtaining higher moments of delay such as variance and skewness to capture the QoS parameters such as jitters in recently popular multimedia applications. Secondly, using the obtained single node media access delay distribution, we extend our modeling approach to investigate the delay in multi-hop networks. Moreover, probabilities of collisions in both hidden and exposed terminal conditions have been calculated. The validity of the model is demonstrated by comparing results predicted by the analytical model against those obtained through simulation experiments.