FASTER ALGORITHMS FOR STABLE ALLOCATION PROBLEMS

We consider a high-multiplicity generalization of the classical stable matching problem known as the stable allocation problem, introduced by Baiou and Balinski in 2002. By leveraging new structural properties and sophisticated data structures, we show how to solve this problem in O(mlog n) time on an bipartite instance with n nodes and m edges, improving the best known running time of O(mn). Our approach simplifies the algorithmic landscape for this problem by providing a common generalization of two different approaches from the literature -- the classical Gale-Shapley algorithm, and a recent algorithm of Baiou and Balinski. Building on this algorithm, we provide an O(m log n) algorithm for the non-bipartite stable allocation problem that introduces a new and useful transformation from non-bipartite to bipartite instances. We also give a polynomial-time algorithm for solving the \u27optimal\u27 variant of the bipartite stable allocation problem, as well as a 2-approximation algorithm for the NP-hard \u27optimal\u27 variant of the non-bipartite stable allocation problem. Finally, we highlight some important connections between the stable allocation problem and the maximum flow problem

A Multi-Game Framework for Harmonized LTE-U and WiFi Coexistence over Unlicensed Bands

The introduction of LTE over unlicensed bands (LTE-U) will enable LTE base stations (BSs) to boost their capacity and offload their traffic by exploiting the underused unlicensed bands. However, to reap the benefits of LTE-U, it is necessary to address various new challenges associated with LTE-U and WiFi coexistence. In particular, new resource management techniques must be developed to optimize the usage of the network resources while handling the interdependence between WiFi and LTE users and ensuring that WiFi users are not jeopardized. To this end, in this paper, a new game theoretic tool, dubbed as \emph{multi-game} framework is proposed as a promising approach for modeling resource allocation problems in LTE-U. In such a framework, multiple, co-existing and coupled games across heterogeneous channels can be formulated to capture the specific characteristics of LTE-U. Such games can be of different properties and types but their outcomes are largely interdependent. After introducing the basics of the multi-game framework, two classes of algorithms are outlined to achieve the new solution concepts of multi-games. Simulation results are then conducted to show how such a multi-game can effectively capture the specific properties of LTE-U and make of it a "friendly" neighbor to WiFi.Comment: Accepted for publication at IEEE Wireless Communications Magazine, Special Issue on LTE in Unlicensed Spectru

Shrewd Selection Speeds Surfing: Use Smart EXP3!

In this paper, we explore the use of multi-armed bandit online learning techniques to solve distributed resource selection problems. As an example, we focus on the problem of network selection. Mobile devices often have several wireless networks at their disposal. While choosing the right network is vital for good performance, a decentralized solution remains a challenge. The impressive theoretical properties of multi-armed bandit algorithms, like EXP3, suggest that it should work well for this type of problem. Yet, its real-word performance lags far behind. The main reasons are the hidden cost of switching networks and its slow rate of convergence. We propose Smart EXP3, a novel bandit-style algorithm that (a) retains the good theoretical properties of EXP3, (b) bounds the number of switches, and (c) yields significantly better performance in practice. We evaluate Smart EXP3 using simulations, controlled experiments, and real-world experiments. Results show that it stabilizes at the optimal state, achieves fairness among devices and gracefully deals with transient behaviors. In real world experiments, it can achieve 18% faster download over alternate strategies. We conclude that multi-armed bandit algorithms can play an important role in distributed resource selection problems, when practical concerns, such as switching costs and convergence time, are addressed.Comment: Full pape

Newton-Raphson Consensus for Distributed Convex Optimization

We address the problem of distributed uncon- strained convex optimization under separability assumptions, i.e., the framework where each agent of a network is endowed with a local private multidimensional convex cost, is subject to communication constraints, and wants to collaborate to compute the minimizer of the sum of the local costs. We propose a design methodology that combines average consensus algorithms and separation of time-scales ideas. This strategy is proved, under suitable hypotheses, to be globally convergent to the true minimizer. Intuitively, the procedure lets the agents distributedly compute and sequentially update an approximated Newton- Raphson direction by means of suitable average consensus ratios. We show with numerical simulations that the speed of convergence of this strategy is comparable with alternative optimization strategies such as the Alternating Direction Method of Multipliers. Finally, we propose some alternative strategies which trade-off communication and computational requirements with convergence speed.Comment: 18 pages, preprint with proof

Fast-Convergent Learning-aided Control in Energy Harvesting Networks

In this paper, we present a novel learning-aided energy management scheme ($\mathtt{LEM}$) for multihop energy harvesting networks. Different from prior works on this problem, our algorithm explicitly incorporates information learning into system control via a step called \emph{perturbed dual learning}. $\mathtt{LEM}$ does not require any statistical information of the system dynamics for implementation, and efficiently resolves the challenging energy outage problem. We show that $\mathtt{LEM}$ achieves the near-optimal $[O(\epsilon), O(\log(1/\epsilon)^2)]$ utility-delay tradeoff with an $O(1/\epsilon^{1-c/2})$ energy buffers ($c\in(0,1)$). More interestingly, $\mathtt{LEM}$ possesses a \emph{convergence time} of $O(1/\epsilon^{1-c/2} +1/\epsilon^c)$, which is much faster than the $\Theta(1/\epsilon)$ time of pure queue-based techniques or the $\Theta(1/\epsilon^2)$ time of approaches that rely purely on learning the system statistics. This fast convergence property makes $\mathtt{LEM}$ more adaptive and efficient in resource allocation in dynamic environments. The design and analysis of $\mathtt{LEM}$ demonstrate how system control algorithms can be augmented by learning and what the benefits are. The methodology and algorithm can also be applied to similar problems, e.g., processing networks, where nodes require nonzero amount of contents to support their actions

Guest editorial: Special issue on matching under preferences

No abstract available

Matching under Preferences

Matching theory studies how agents and/or objects from different sets can be matched with each other while taking agents\u2019 preferences into account. The theory originated in 1962 with a celebrated paper by David Gale and Lloyd Shapley (1962), in which they proposed the Stable Marriage Algorithm as a solution to the problem of two-sided matching. Since then, this theory has been successfully applied to many real-world problems such as matching students to universities, doctors to hospitals, kidney transplant patients to donors, and tenants to houses. This chapter will focus on algorithmic as well as strategic issues of matching theory. Many large-scale centralized allocation processes can be modelled by matching problems where agents have preferences over one another. For example, in China, over 10 million students apply for admission to higher education annually through a centralized process. The inputs to the matching scheme include the students\u2019 preferences over universities, and vice versa, and the capacities of each university. The task is to construct a matching that is in some sense optimal with respect to these inputs. Economists have long understood the problems with decentralized matching markets, which can suffer from such undesirable properties as unravelling, congestion and exploding offers (see Roth and Xing, 1994, for details). For centralized markets, constructing allocations by hand for large problem instances is clearly infeasible. Thus centralized mechanisms are required for automating the allocation process. Given the large number of agents typically involved, the computational efficiency of a mechanism's underlying algorithm is of paramount importance. Thus we seek polynomial-time algorithms for the underlying matching problems. Equally important are considerations of strategy: an agent (or a coalition of agents) may manipulate their input to the matching scheme (e.g., by misrepresenting their true preferences or underreporting their capacity) in order to try to improve their outcome. A desirable property of a mechanism is strategyproofness, which ensures that it is in the best interests of an agent to behave truthfully