In the past year or so, an exciting progress has led to throughput optimal design of CSMA-based algorithms for wireless networks. However, such an algorithm suffers from very poor delay performance. A recent work suggests that it is impossible to design a CSMA-like simple algorithm that is throughput optimal and induces low delay for any wireless network. However, wireless networks arising in practice are formed by nodes placed, possibly arbitrarily, in some geographic area. In this paper, we propose a CSMA algorithm with per-node average-delay bounded by a constant, independent of the network size, when the network has geometry (precisely, polynomial growth structure) that is present in any practical wireless network. Two novel features of our algorithm, crucial for its performance, are (a) choice of access probabilities as an appropriate function of queue-sizes, and (b) use of local network topological structures. Essentially, our algorithm is a queue-based CSMA with a minor difference that at each time instance a very small fraction of frozen nodes do not execute CSMA. Somewhat surprisingly, appropriate selection of such frozen nodes, in a distributed manner, lead to the delay optimal performance.

We study multi-armed bandit (MAB) problems with additional observations, where in each round, the decision maker selects an arm to play and can also observe rewards of additional arms (within a given budget) by paying certain costs. In the case of stochastic rewards, we develop a new algorithm KL-UCB-AO which is asymptotically optimal when the time horizon grows large, by smartly identifying the optimal set of the arms to be explored using the given budget of additional observations. In the case of adversarial rewards, we propose H-INF, an algorithm with order-optimal regret. H-INF exploits a two-layered structure where in each layer, we run a known optimal MAB algorithm. Such a hierarchical structure facilitates the regret analysis of the algorithm, and in turn, yields order-optimal regret. We apply the framework of MAB with additional observations to the design of rate adaptation schemes in 802.11-like wireless systems, and to that of online advertisement systems. In both cases, we demonstrate that our algorithms leverage additional observations to significantly improve the system performance. We believe the techniques developed in this paper are of independent interest for other MAB problems, e.g., contextual or graph-structured MAB.

A variety of models have been proposed and analyzed to understand how a new innovation (e.g., a technology, a product, or even a behavior) diffuses over a social network, broadly classified into either of epidemic-based or game-based ones. In this paper, we consider a game-based model, where each individual makes a selfish, rational choice in terms of its payoff in adopting the new innovation, but with some noise. We study how diffusion effect can be maximized by seeding a subset of individuals (within a given budget), i.e., convincing them to pre-adopt a new innovation. In particular, we aim at finding `good' seeds for minimizing the time to infect all others, i.e., diffusion speed maximization . To this end, we design polynomial-time approximation algorithms for three representative classes, Erdőos-Réenyi, planted partition and geometrically structured graph models, which correspond to globally well-connected, locally well-connected with large clusters and locally well-connected with small clusters, respectively, provide their performance guarantee in terms of approximation and complexity. First, for the dense Erdős-Rényi and planted partition graphs, we show that an arbitrary seeding and a simple seeding proportional to the size of clusters are almost optimal with high probability. Second, for geometrically structured sparse graphs, including planar and d -dimensional graphs, our algorithm that (a) constructs clusters, (b) seeds the border individuals among clusters, and (c) greedily seeds inside each cluster always outputs an almost optimal solution. We validate our theoretical findings with extensive simulations under a real social graph. We believe that our results provide new practical insights on how to seed over a social network depending on its connection structure, where individuals rationally adopt a new innovation. To our best knowledge, we are the first to study such diffusion speed maximization on the game-based diffusion, while the extensive research efforts have been made in epidemic-based models, often referred to as influence maximization .

The popularity of Aloha -like algorithms for resolution of contention between multiple entities accessing common resources is due to their extreme simplicity and distributed nature. Example applications of such algorithms include Ethernet and recently emerging wireless multi-access networks. Despite a long and exciting history of more than four decades, the question of designing an algorithm that is essentially as simple and distributed as Aloha while being efficient has remained unresolved. In this paper, we resolve this question successfully for a network of queues where contention is modeled through independent-set constraints over the network graph. The work by Tassiulas and Ephremides (1992) suggests that an algorithm that schedules queues so that the summation of `weight' of scheduled queues is maximized, subject to constraints, is efficient. However, implementing such an algorithm using Aloha-like mechanism has remained a mystery. We design such an algorithm building upon a Metropolis-Hastings sampling mechanism along with selection of `weight' as an appropriate function of the queue-size. The key ingredient in establishing the efficiency of the algorithm is a novel adiabatic -like theorem for the underlying queueing network, which may be of general interest in the context of dynamical systems.

Since Tassiulas and Ephremides proposed the maximum weight scheduling algorithm of throughput-optimality for constrained queueing networks in 1992, extensive research efforts have been made for resolving its high complexity issue under various directions. In this paper, we resolve this issue by developing a generic framework for designing throughput-optimal and low-complexity scheduling algorithms. Under the framework, an algorithm updates current schedules via an interaction with a given oracle system that generates a solution of a certain discrete optimization problem in a finite number of interactive queries. The complexity of the resulting algorithm is decided by the number of operations required for an oracle processing a single query, which is typically very small. Somewhat surprisingly, we prove that an algorithm using any such oracle is throughput-optimal for general constrained queueing network models that arise in the context of emerging large-scale communication networks. To our best knowledge, our result is the first that establishes a rigorous connection between iterative optimization methods and low-complexity scheduling algorithms, which we believe provides various future directions and new insights in both areas.