In data-intensive applications, graphs serve as foundational structures across various domains. However, the increasing size of datasets poses significant challenges to performing downstream tasks. To address this problem, techniques such as graph coarsening, condensation, and summarization have been developed to create a coarsened graph while preserving important properties of the original graph by considering both the graph matrix and the feature or attribute matrix of the original graph as inputs. However, existing graph coarsening techniques often neglect the label information during the coarsening process, which can result in a lower-quality coarsened graph and limit its suitability for downstream tasks. To overcome this limitation, we introduce the Label-Aware Graph Coarsening (LAGC) algorithm, a semi-supervised approach that incorporates the graph matrix, feature matrix, and some of the node label information to learn a coarsened graph. Our proposed formulation is a non-convex optimization problem that is efficiently solved using block successive upper bound minimization(BSUM) technique, and it is provably convergent. Our extensive results demonstrate that the LAGC algorithm outperforms the existing state-of-the-art method by a significant margin.

The popularity of edge computing has risen due to the widespread use of online services on IoT and mobile devices. This technology provides geographically distributed edge servers to reduce delays, energy consumption, and bandwidth requirements. However, edge computing faces challenges due to limited computing resources on edge servers and the dynamic density of IoT and mobile device users. In this article, we propose a distributed edge resource allocation approach that can accommodate the dynamic user population on the limited computing resources of edge servers. Our proposed approach aims to balance the loads of edge servers to maximize resource utilization by moving users from overloaded edge servers to underutilized ones. This way, edge computing resources can serve the maximum number of users. In addition, the proposed approach identifies bottleneck resources on edge servers to maintain the quality of service (QoS) provided by the edge servers. Thus, this approach ensures that users' experience remains consistent and meets the required QoS standards. We also validate the performance of the proposed algorithm by simulating it and simulation results show that the approach achieves its objectives and improves the efficiency of edge computing resources compared to state-of-the-art approaches.

This article addresses the Edge User Allocation (EUA) problem in edge computing, where the appropriate mapping from users to edge servers (ESs) is crucial for optimizing performance metrics. Game theory is one of the powerful tools used in edge computing for user allocation to edge resources and task offloading. However, this approach takes longer to converge to Pure Nash Equilibrium (PNE), which is called a stable optimal solution. In this article, we propose a grouping technique for ESs, enabling parallel execution of game-theoretic approaches to achieve faster convergence at the PNE. Our contributions include the grouping method, the introduction of parallel Best Response (BR) dynamics for rapid convergence, and proof that the parallel BR dynamics will eventually halt at PNE. We also provide empirical evidence demonstrating its efficiency compared to traditional BR dynamics. This research enhances the scalability and effectiveness of game-theoretic approaches in resolving the EUA problem, offering practical solutions for edge computing scenarios.

In edge computing, the app vendors hire resources from edge servers and allocate them to app users to overcome the challenge of the limited computing capacities of their IoT devices. An app vendor intends to provide app services to the maximum number of users with the least number of edge servers in order to make efficient use of edge resources while reducing overall system costs. However, when an edge server has to serve more app users than its capacity, the Quality of Service (QoS) deteriorates. Thus, establishing a tradeoff between cost and QoS is a critical challenge in the process of allocating edge computing resources to users. It is referred to as the app user allocation (AUA) problem. To solve the AUA problem, we propose a distributed game-theoretic approach that finds a pure Nash equilibrium (PNE) as the optimal stable solution. We first model the AUA problem as a constrained optimization problem and then introduce a user allocation game (UAGame) to solve it. This UAGame employs a distributed edge server allocation (ESA) algorithm to reach PNE. The time complexity of the ESA algorithm is reduced by the edge server clustering. It has also been shown that the UAGame is a potential game, and therefore the ESA algorithm is guaranteed to converge at PNE. The performance of the ESA algorithm has also been studied theoretically and validated numerically.

Internet of Things (IoT) devices have enabled communications in resource-limited computing environments. Sensor nodes from the multiple IoT devices collectively work for many applications, such as disaster management, border security management, smart farming, smart cities, etc. In such applications, the data from a single source node is often destined for multiple nodes. Multicast communication is preferred over unicast or broadcast communication for such applications, as multicast uses fewer resources. Efficient construction of the multicast tree leads to cost-effective multicast transmission. This article introduces a path selection game (PSGame), a game-theoretic approach that formulates the construction problem of the least-cost multicast tree as a potential game. Our proposed path selection algorithm (PSA) quickly converges to the pure Nash equilibrium (PNE), bringing the least cost multicast tree. Our findings show that the overhead incurred in terms of energy consumption and delay is minimal in the proposed algorithm compared to other mechanisms. The theoretical analysis proves that the proposed algorithm quickly converges to PNE in$O(n.r_{\max })$steps. It also proves that the cost ratio between the proposed solution and the centralized optimum will be bounded by$\log (n)$. The numerical analysis substantiates the theoretical analysis.

The research paper [1] proposes a differential privacy algorithm in the context of Federated Learning and provides its performance analysis, mainly focusing on proving a convergence bound for the loss function. In this paper, we show that some of the mathematical derivations given in [1] are not valid. Thus the bounds they prove in the paper do not hold for all loss functions. In this work, we give the correct derivation of the best possible local sensitivity bound, which is valid for all loss functions. We also state the modifications in the bounds for global sensitivity and the standard deviation of the Gaussian noise added, both before and after aggregation.

In a peer-to-peer system, a node should estimate reputation of other peers not only on the basis of its own interaction, but also on the basis of experience of other nodes. Reputation aggregation mechanism implements strategy for achieving this. Reputation aggregation in peer to peer networks is generally a very time and resource consuming process. This paper proposes a reputation aggregation algorithm that uses a variant of gossip algorithm called differential gossip. In this paper, estimate of reputation is considered to be having two parts, one common component which is same with every node, and the other one is the information received from immediate neighbours based on the neighbours' direct interaction with the node. Theoretical analysis and numerical results show that differential gossip is fast and requires lesser amount of resources. The reputation computed using the proposed algorithm also shows a good amount of immunity to the collusion.

In a peer-to-peer system, a node should estimate reputation of other peers not only on the basis of its own interaction, but also on the basis of expression of other nodes. Reputation aggregation mechanism implements strategy for achieving this. Reputation aggregation in peer to peer networks is generally a very time and resource consuming process. Moreover, most of the methods consider that a node will have the same reputation after aggregation with all the nodes in the network, which is not true. This paper proposes a reputation aggregation algorithm that uses a variant of gossip algorithm called differential gossip. In this paper, estimate of reputation is considered to be having two parts, one common component which is same with every node, and the other one is the information received from immediate neighbours based on the neighbours' direct interaction with the node. The differential gossip is fast and requires a lesser amount of resources. This mechanism allows computation of independent reputation value by every node, of every other node in the network. The differential gossip trust has been investigated for a power law network formed using preferential attachment (PA) Model. The reputation computed using differential gossip trust shows good amount of immunity to the collusion. We have verified the performance of the algorithm on the power law networks with sizes ranging from 100 nodes to 50,000 nodes.