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1. Interactive Distributed Proofs

   Kol, Gillat; Oshman, Rotem; Saxena, Raghuvansh. (January 2018, ACM Symposium on Principles of Distributed Computing)

   Interactive proof systems allow a resource-bounded verifier to decide an intractable language (or compute a hard function) by communicating with a powerful but untrusted prover. Such systems guarantee that the prover can only convince the verifier of true statements. In the context of centralized computation, a celebrated result shows that interactive proofs are extremely powerful, allowing polynomial-time verifiers to decide any language in PSPACE. In this work we initiate the study of interactive distributed proofs: a network of nodes interacts with a single untrusted prover, who sees the entire network graph, to decide whether the graph satisfies some property. We focus on the communication cost of the protocol — the number of bits the nodes must exchange with the prover and each other. Our model can also be viewed as a generalization of the various models of “distributed NP” (proof labeling schemes, etc.) which received significant attention recently: while these models only allow the prover to present each network node with a string of advice, our model allows for back-and-forth interaction. We prove both upper and lower bounds for the new model. We show that for some problems, interaction can exponentially decrease the communication cost compared to a non-interactive prover, but on the other hand, some problems retain non-trivial cost even with interaction. 

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2. Neighborhood-based bridge node centrality tuple for complex network analysis

   https://doi.org/10.1007/s41109-021-00388-1  

   Meghanathan, Natarajan (December 2021, Applied Network Science)

   Abstract We define a bridge node to be a node whose neighbor nodes are sparsely connected to each other and are likely to be part of different components if the node is removed from the network. We propose a computationally light neighborhood-based bridge node centrality (NBNC) tuple that could be used to identify the bridge nodes of a network as well as rank the nodes in a network on the basis of their topological position to function as bridge nodes. The NBNC tuple for a node is asynchronously computed on the basis of the neighborhood graph of the node that comprises of the neighbors of the node as vertices and the links connecting the neighbors as edges. The NBNC tuple for a node has three entries: the number of components in the neighborhood graph of the node, the algebraic connectivity ratio of the neighborhood graph of the node and the number of neighbors of the node. We analyze a suite of 60 complex real-world networks and evaluate the computational lightness, effectiveness, efficiency/accuracy and uniqueness of the NBNC tuple vis-a-vis the existing bridgeness related centrality metrics and the Louvain community detection algorithm. 

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3. GraphTM: An Efficient Framework for Supporting Transactional Memory in a Distributed Environment

   https://doi.org/10.1145/3369740.3369774  

   Poudel, Pavan; Sharma, Gokarna (January 2020, The 21st International Conference on Distributed Computing and Networking (ICDCN))

   In this paper, we present GraphTM, an efficient and scalable framework for processing transactions in a distributed environment. The distributed environment is modeled as a graph where each node of the graph is a processing node that issues transactions. The objects that transactions use to execute are also on the graph nodes (the initial placement may be arbitrary). The transactions execute on the nodes which issue them after collecting all the objects that they need following the data-flow model of computation. This collection is done by issuing the requests for the objects as soon as transaction starts and wait until all required objects for the transaction come to the requesting node. The challenge is on how to schedule the transactions so that two crucial performance metrics, namely (i) total execution time to commit all the transactions, and (ii) total communication cost involved in moving the objects to the requesting nodes, are minimized. We implemented GraphTM in Java and assessed its performance through 3 micro-benchmarks and 5 complex benchmarks from STAMP benchmark suite on 5 different network topologies, namely, clique, line, grid, cluster, and star, that make an underlying communication network for a representative set of distributed systems commonly used in practice. The results show the efficiency and scalability of our approach. 

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4. Reliable Spanners for Metric Spaces

   https://doi.org/10.1145/3563356  

   Har-Peled, Sariel; Mendel, Manor; Oláh, Dániel (January 2023, ACM Transactions on Algorithms)

   A spanner is reliable if it can withstand large, catastrophic failures in the network. More precisely, any failure of some nodes can only cause a small damage in the remaining graph in terms of the dilation. In other words, the spanner property is maintained for almost all nodes in the residual graph. Constructions of reliable spanners of near linear size are known in the low-dimensional Euclidean settings. Here, we present new constructions of reliable spanners for planar graphs, trees, and (general) metric spaces. 

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5. Learn Locally, Correct Globally: A Distributed Algorithm for Training Graph Neural Networks

   Morteza Ramezani, Weilin Cong (April 2022, International Conference on Learning (ICLR))

   Despite the recent success of Graph Neural Networks (GNNs), training GNNs on large graphs remains challenging. The limited resource capacities of the existing servers, the dependency between nodes in a graph, and the privacy concern due to the centralized storage and model learning have spurred the need to design an effective distributed algorithm for GNN training. However, existing distributed GNN training methods impose either excessive communication costs or large memory overheads that hinders their scalability. To overcome these issues, we propose a communication-efficient distributed GNN training technique named (LLCG). To reduce the communication and memory overhead, each local machine in LLCG first trains a GNN on its local data by ignoring the dependency between nodes among different machines, then sends the locally trained model to the server for periodic model averaging. However, ignoring node dependency could result in significant performance degradation. To solve the performance degradation, we propose to apply on the server to refine the locally learned models. We rigorously analyze the convergence of distributed methods with periodic model averaging for training GNNs and show that naively applying periodic model averaging but ignoring the dependency between nodes will suffer from an irreducible residual error. However, this residual error can be eliminated by utilizing the proposed global corrections to entail fast convergence rate. Extensive experiments on real-world datasets show that LLCG can significantly improve the efficiency without hurting the performance. One-sentence Summary: We propose LLCG a communication efficient distributed algorithm for training GNNs. 

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