In this article, we propose two distributed iterative algorithms that can be used to solve the distributed optimization problem for quadratic local cost functions over large-scale networks in finite time. The first algorithm exhibits synchronous operation while the second one exhibits asynchronous operation. Both algorithms operate exclusively with quantized values. This means that the information stored, processed, and exchanged between neighboring nodes is subject to deterministic uniform quantization. The algorithms rely on event-driven updates in order to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage. Finally, once the algorithms converge, nodes distributively terminate their operation. We prove that our algorithms converge in a finite number of iterations to the exact optimal solution depending on the quantization level, and we present applications of our algorithms to, first, optimal task scheduling for data centers, and second, global model aggregation for distributed federated learning. We provide simulations of these applications to illustrate the operation, performance, and advantages of the proposed algorithms. In addition, it is shown that our proposed algorithms compare favorably to algorithms in the current literature.

We consider the problems of computing the average degree and the size of a given network in a distributed fashion and under quantized communication. More specifically, we present two distributed algorithms, which rely on quantized operation (i.e., nodes process and transmit quantized messages) and are able to obtain the exact solutions in a finite number of steps. During the operation of our algorithms, each node can determine in a distributed manner whether convergence has been achieved and correspondingly terminate its operation. For terminating the operation of our algorithms, we assume a known bound for the network diameter. To the best of the authors' knowledge, these algorithms are the first to find exact solutions (i.e., with no error in the final result) under quantized communication. Note that our network size calculation algorithm is the first in the literature to calculate the exact size of a network in a finite number of steps without introducing a final error; in other algorithms, this error can be either due to quantization or asymptotic convergence. In our case, no error is introduced since the desired result is calculated in the form of a fraction involving an integer numerator and an integer denominator. We demonstrate the operation of our algorithms and their potential advantages through simulations.

In this paper, we consider the problem of privacy preservation in the average consensus problem when communication among nodes is quantized. More specifically, we consider a setting where nodes in the network can be curious, while certain nodes in the network want to ensure that their initial states cannot be inferred exactly by these curious nodes. Curious nodes are not malicious, i.e., they try to identify the initial states of other nodes based on the data they receive during their operation (and some of them might even collude) but do not interfere in the computation in any other way. Each node in the network (including curious nodes) can opt to execute a privacy-preserving algorithm (so as not to reveal the initial state it contributes to the average calculation) or its underlying (plain) average consensus algorithm (if privacy is not a concern). We propose two privacy-preserving event-triggered quantized average consensus algorithms. Under certain topological conditions, both proposed algorithms allow the nodes who adopt privacy-preserving protocols to preserve their privacy and at the same time to obtain, after a finite number of steps, the exact average of the initial states while processing and transmitting <italic>quantized</italic> information. We also present illustrative examples and comparisons of our algorithms against other algorithms in the existing literature, and discuss a motivating application in which smart meters in a smart grid collect real-time demands in a privacy-preserving manner. 

In this paper, we consider the unconstrained distributed optimization problem, in which the exchange of information in the network is captured by a directed graph topology, thus, nodes can only communicate with their neighbors. Additionally, in our problem, the communication channels among the nodes have limited bandwidth. In order to alleviate this limitation, quantized messages should be exchanged among the nodes. For solving this distributed optimization problem, we combine a gradient descent method with a distributed quantized consensus algorithm (which requires the nodes to exchange quantized messages and converges in a finite number of steps). Specifically, at every optimization step, each node (i) performs a gradient descent step (i.e., subtracts the scaled gradient from its current estimate), and (ii) performs a finite-time calculation of the quantized average of every node's estimate in the network. As a consequence, this algorithm approximately mimics the centralized gradient descent algorithm. We show that our algorithm asymptotically converges to a neighborhood of the optimal solution with linear convergence rate. The performance of the proposed algorithm is demonstrated via simple illustrative examples.

This paper considers a network of collaborating agents for local resource allocation subject to nonlinear model constraints. In many applications, it is required (or desirable) that the solution be anytime feasible in terms of satisfying the sum-preserving global constraint. Motivated by this, sufficient conditions on the nonlinear mapping for anytime feasibility (or non-asymptotic feasibility) are addressed in this paper. For the two proposed distributed solutions, one converges over directed weight-balanced networks and the other one over undirected networks. In particular, we elaborate on uniform quantization and discuss the notion of ϵ-accurate solution, which gives an estimate of how close we can get to the exact optimizer subject to different quantization levels. This work, further, handles general (possibly non-quadratic) strictly convex objective functions with application to CPU allocation among a cloud of data centers via distributed solutions. The results can be used as a coordination mechanism to optimally balance the tasks and CPU resources among a group of networked servers while addressing quantization or limited server capacity.

In this paper, we present a distributed version of the k-means algorithm for multi-agent systems with directed communication links. The goal of k-means is to partition the network's agents in mutually exclusive sets (groups) such that agents in the same set have (and possibly share) similar information and are able to calculate a representative value for their group. Our distributed algorithm allows each node to transmit quantized values in an event-driven fashion, and exhibits distributed stopping capabilities. Transmitting quantized values leads to more efficient usage of the available bandwidth and reduces the communication bottleneck, whereas distributed stopping preserves available resources. We characterize the properties of the proposed distributed algorithm and show that its execution (on any static and strongly connected digraph) will partition all agents in mutually exclusive clusters in finite time. We conclude with examples that illustrate the operation, performance, and potential advantages of the proposed algorithm.

In this article, we propose a distributed negotiation framework that allows a set of cooperative agents to find a common ground with their neighbors while attempting to modify their initial opinion by the least possible amount. Based on such a framework, we develop a distributed agreement approach where the effort spent in the local agreement reflects the relevance of the agents in a weighted consensus process. In particular, we assume that players whose ideas happen to satisfactory mediate the standpoint of their interlocutors will end-up being more influential in the overall decision-making process. We conclude the article by applying the proposed methodology in the context of distributed data aggregation scenarios, as a way to mitigate the effect of outliers (e.g., faulty sensors).

In this paper, we analyze the problem of optimally allocating resources in a distributed and privacy-preserving manner. We propose a novel distributed optimal resource allocation algorithm with privacy-preserving guarantees, which operates over a directed communication network. Our algorithm converges in finite time and allows each node to process and transmit quantized messages. Our algorithm utilizes a distributed quantized average consensus strategy combined with a privacy-preserving mechanism. We show that the algorithm converges in finite-time, and we prove that, under specific conditions on the network topology, nodes are able to preserve the privacy of their initial state. Finally, to illustrate the results, we consider an example where test kits need to be optimally allocated proportionally to the number of infections in a region. It is shown that the proposed privacy-preserving resource allocation algorithm performs well with an appropriate convergence rate under privacy guarantees. Copyright

In this paper, we focus on the problem of data sharing over a wireless computer network (i.e., a wireless grid). Given a set of available data, we present a distributed algorithm, which operates over a dynamically changing network and allows each node to calculate the optimal allocation of data in a finite number of time steps. We show that our proposed algorithm (i) converges to the optimal solution in finite time with very high probability, and (ii) once the optimal solution is reached, each node is able to cease transmissions without needing knowledge of a global parameter such as the network diameter. Furthermore, our algorithm (i) operates exclusively with quantized values (i.e., each node processes and transmits quantized information), (ii) relies on event-driven updates, and (iii) calculates the optimal solution in the form of a quantized fraction which avoids errors due to quantization. Finally, we demonstrate the operation, performance, and potential advantages of our algorithm over random dynamic networks.

We consider a flow network that is described by a digraph, each edge of which can admit a flow within a certain interval, with nonnegative end points that correspond to lower and upper flow limits. We propose and analyze a distributed iterative algorithm for solving, in {\em finite time}, the so-called feasible circulation problem, which consists of computing flows that are {\em admissible} (i.e., within the given intervals at each edge) and {\em balanced} (i.e., the total in-flow equals the total out-flow at each node). The algorithm assumes a communication topology that allows bidirectional message exchanges between pairs of nodes that are physically connected (i.e., nodes that share a directed edge in the physical topology) and is shown to converge to a feasible and balanced solution as long as the necessary and sufficient circulation conditions are satisfied with strict inequality. In case the initial flows and flow limits are commensurable (i.e., they are integer multiples of a given constant), then the proposed algorithm reduces to a previously proposed finite-time balancing algorithm, for which we provide an explicit bound on the number of steps required for termination.