Given an initial resource allocation, where some agents may envy others or where a different distribution of resources might lead to higher social welfare, our goal is to improve the allocation without reassigning resources. We consider a sharing concept allowing resources being shared with social network neighbors of the resource owners. To this end, we introduce a formal model that allows a central authority to compute an optimal sharing between neighbors based on an initial allocation. Advocating this point of view, we focus on the most basic scenario where a resource may be shared by two neighbors in a social network and each agent can participate in a bounded number of sharings. We present algorithms for optimizing utilitarian and egalitarian social welfare of allocations and for reducing the number of envious agents. In particular, we examine the computational complexity with respect to several natural parameters. Furthermore, we study cases with restricted social network structures and, among others, devise polynomial-time algorithms in path- and tree-like (hierarchical) social networks.
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We introduce the problem of finding a set $B$ of $k$ points in $[0,1]^n$ such that the expected cost of the cheapest point in $B$ that dominates a random point from $[0,1]^n$ is minimized. We study the case where the coordinates of the random points are independently distributed and the cost function is linear. This problem arises naturally in various application areas where customers' requests are satisfied based on predefined products, each corresponding to a subset of features. We show that the problem is NP-hard already for $k=2$ when each coordinate is drawn from $\{0,1\}$, and obtain an FPTAS for general fixed $k$ under mild assumptions on the distributions.
Every computer system -- from schedulers in clouds (e.g. Amazon) to computer networks to operating systems -- performs resource allocation across system users. The defacto allocation policies are max-min fairness (MMF) for single resources and dominant resource fairness (DRF) for multiple resources which guarantee properties like incentive compatibility, envy-freeness, and Pareto efficiency, assuming user demands are static (time-independent). However, in real-world systems, user demands are dynamic, i.e. time-dependant. As a result, there is now a fundamental mismatch between the goals of computer systems and the properties enabled by classic resource allocation policies. We aim to bridge this mismatch. When demands are dynamic, instant-by-instant MMF can be extremely unfair over longer periods of time, i.e. lead to unbalanced user allocations as previous allocations have no effect in the present. We consider a natural generalization of MMF and DRF for multiple resources and users with dynamic demands: this algorithm ensures that user allocations are as max-min fair as possible up to any time instant, given past allocations. This dynamic mechanism remains Pareto optimal and envy-free, but not incentive compatible. However, our results show that the possible increase in utility by misreporting is bounded and, since this can lead to significant decrease in overall useful allocation, this suggests that it is not a useful strategy. Our main result is to show that our dynamic DRF algorithm is $(1+\rho)$-incentive compatible, where $\rho$ quantifies the relative importance of a resource for different users; we show that this factor is tight even with only two resources. We also present a $3/2$ upper bound and a $\sqrt 2$ lower bound for incentive compatibility when there is only one resource. We also offer extensions for the case when users are weighted to prioritize them differently.
The emerging edge computing paradigm promises to provide low latency and ubiquitous computation to numerous mobile and Internet of Things (IoT) devices at the network edge. How to efficiently allocate geographically distributed heterogeneous edge resources to a variety of services is a challenging task. While this problem has been studied extensively in recent years, most of the previous work has largely ignored the preferences of the services when making edge resource allocation decisions. To this end, this paper introduces a novel bilevel optimization model, which explicitly takes the service preferences into consideration, to study the interaction between an EC platform and multiple services. The platform manages a set of edge nodes (ENs) and acts as the leader while the services are the followers. Given the service placement and resource pricing decisions of the leader, each service decides how to optimally divide its workload to different ENs. The proposed framework not only maximizes the profit of the platform but also minimizes the cost of every service. When there is a single EN, we derive a simple analytic solution for the underlying problem. For the general case with multiple ENs and multiple services, we present a Karush Kuhn Tucker based solution and a duality based solution, combining with a series of linearizations, to solve the bilevel problem. Extensive numerical results are shown to illustrate the efficacy of the proposed model.
We investigate the implementation of reduced-form allocation probabilities in a two-person bargaining problem without side payments, where the agents have to select one alternative from a finite set of social alternatives. We provide a necessary and sufficient condition for the implementability. We find that the implementability condition in bargaining has some new feature compared to Border's theorem. Our results have applications in compromise problems and package exchange problems where the agents barter indivisible objects and the agents value the objects as complements.
We propose a generic mechanism for incentivizing behavior in an arbitrary finite game using payments. Doing so is trivial if the mechanism is allowed to observe all actions taken in the game, as this allows it to simply punish those agents who deviate from the intended strategy. Instead, we consider an abstraction where the mechanism probabilistically infers information about what happened in the game. We show that payment schemes can be used to implement any set of utilities if and only if the mechanism can essentially infer completely what happened. We show that finding an optimal payment scheme for games of perfect information is \textsf{P}-complete, and conjecture it to be \textsf{PPAD}-hard for games of imperfect information. We prove a lower bound on the size of the payments, showing that the payments must be linear in the intended level of security. We demonstrate the applicability of our model to concrete problems in distributed computing, namely decentralized commerce and secure multiparty computation, for which the payments match the lower bound asymptotically.
We introduce a modular verification approach to network control plane verification, where we cut a network into smaller fragments to improve the scalability of SMT solving. Users provide an annotated cut which describes how to generate these fragments from the monolithic network, and we verify each fragment independently, using the annotations to define assumptions and guarantees over fragments akin to assume-guarantee reasoning. We prove this modular network verification procedure is sound and complete with respect to verification over the monolithic network. We implement this procedure as Kirigami, an extension of NV - a network verification language and tool - and evaluate it on industrial topologies with synthesized policies. We observe a 2-8x improvement in end-to-end NV verification time, with SMT solve time improving by up to 6 orders of magnitude.
With the explosive increment of computation requirements, the multi-access edge computing (MEC) paradigm appears as an effective mechanism. Besides, as for the Internet of Things (IoT) in disasters or remote areas requiring MEC services, unmanned aerial vehicles (UAVs) and high altitude platforms (HAPs) are available to provide aerial computing services for these IoT devices. In this paper, we develop the hierarchical aerial computing framework composed of HAPs and UAVs, to provide MEC services for various IoT applications. In particular, the problem is formulated to maximize the total IoT data computed by the aerial MEC platforms, restricted by the delay requirement of IoT and multiple resource constraints of UAVs and HAPs, which is an integer programming problem and intractable to solve. Due to the prohibitive complexity of exhaustive search, we handle the problem by presenting the matching game theory based algorithm to deal with the offloading decisions from IoT devices to UAVs, as well as a heuristic algorithm for the offloading decisions between UAVs and HAPs. The external effect affected by interplay of different IoT devices in the matching is tackled by the externality elimination mechanism. Besides, an adjustment algorithm is also proposed to make the best of aerial resources. The complexity of proposed algorithms is analyzed and extensive simulation results verify the efficiency of the proposed algorithms, and the system performances are also analyzed by the numerical results.
We study the problem of allocating $m$ indivisible items to $n$ agents with additive utilities. It is desirable for the allocation to be both fair and efficient, which we formalize through the notions of envy-freeness and Pareto-optimality. While envy-free and Pareto-optimal allocations may not exist for arbitrary utility profiles, previous work has shown that such allocations exist with high probability assuming that all agents' values for all items are independently drawn from a common distribution. In this paper, we consider a generalization of this model where each agent's utilities are drawn independently from a distribution specific to the agent. We show that envy-free and Pareto-optimal allocations are likely to exist in this asymmetric model when $m=\Omega\left(n\log n\right)$, which is tight up to a log log gap that also remains open in the symmetric subsetting. Furthermore, these guarantees can be achieved by a polynomial-time algorithm.
Fog-assisted 5G Networks allow the users within the networks to execute their tasks and processes through fog nodes and cooperation among the fog nodes. As a result, the delay in task execution reduces as compared to that in case of independent task execution, where the Base Station (BS) or server is directly involved. In the practical scenario, the ability to cooperate clearly depends on the willingness of fog nodes to cooperate. Hence, in this paper, we propose an incentive-based bargaining approach which encourages the fog nodes to cooperate among themselves by receiving incentives from the end users benefitting from the cooperation. Considering the heterogenous nature of users and fog nodes based on their storage capacity, energy efficiency etc., we aim to emphasise a fair incentive mechanism which fairly and uniformly distributes the incentives from user to the participating fog nodes. The proposed incentive-based cooperative approach reduces the cost of end users as well as balances the energy consumption of fog nodes. The proposed system model addresses and models the above approaches and mathematically formulate cost models for both fog nodes and the end users in a fog-assisted 5G network.
To avoid treating neural networks as highly complex black boxes, the deep learning research community has tried to build interpretable models allowing humans to understand the decisions taken by the model. Unfortunately, the focus is mostly on manipulating only the very high-level features associated with the last layers. In this work, we look at neural network architectures for classification in a more general way and introduce an algorithm which defines before the training the paths of the network through which the per-class information flows. We show that using our algorithm we can extract a lighter single-purpose binary classifier for a particular class by removing the parameters that do not participate in the predefined information path of that class, which is approximately 60% of the total parameters. Notably, leveraging coding theory to design the information paths enables us to use intermediate network layers for making early predictions without having to evaluate the full network. We demonstrate that a slightly modified ResNeXt model, trained with our algorithm, can achieve higher classification accuracy on CIFAR-10/100 and ImageNet than the original ResNeXt, while having all the aforementioned properties.
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