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Fault-Tolerant Graph Realizations in the Congested Clique, Revisited

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Book cover Distributed Computing and Intelligent Technology (ICDCIT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13776))

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Abstract

We study the graph realization problem in the Congested Clique in a distributed network under the crash-fault model. We focus on the degree-sequence realization, each node v is associated with a degree value d(v), and the resulting degree sequence is realizable if it is possible to construct an overlay network with the given degrees. This paper focuses on the message and round complexity of deterministic graph realization in the anonymous network. It has been shown by Kumar et al. [ALGOSENSORS 2022] that the graph realization can be solved using \(O(n^2)\) message and O(f) round without the knowledge of f, of which f nodes could be faulty \((f<n)\). However, their algorithm works for \(KT_1\) (Knowledge Till 1 hop) model where nodes know their neighbors’ IDs; or in the \(KT_0\) (Knowledge Till 0 hop) model, in which each node knows the IDs of all the nodes in the clique, but doesn’t know which port is connecting to which node-ID. In this paper, we extend the result to \(KT_0\) when the network is anonymous, i.e., the IDs of the neighboring nodes are unknown. We present an algorithm that solves the graph realization problem in the \(KT_0\) model with matching performance guarantees as in the \(KT_1\) model.

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Notes

  1. 1.

    In contrast, a non-adaptive (static) adversary selects the nodes to be faulty before the execution of the algorithm starts.

  2. 2.

    Node which is in active state (standby state) considered as active node (standby node).

  3. 3.

    A non-faulty setup is the model in which all the nodes are non-faulty.

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Authors and Affiliations

  1. Indian Statistical Institute, Kolkata, India

    Manish Kumar

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  1. Manish Kumar
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Correspondence to Manish Kumar .

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Editors and Affiliations

  1. Indian Statistical Institute, Kolkata, India

    Anisur Rahaman Molla

  2. Kent State University, Kent, OH, USA

    Gokarna Sharma

  3. Indian Institute of Management, Lucknow, India

    Pradeep Kumar

  4. Technology Innovation Institute, Abu Dhabi, United Arab Emirates

    Sanjay Rawat

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Kumar, M. (2023). Fault-Tolerant Graph Realizations in the Congested Clique, Revisited. In: Molla, A.R., Sharma, G., Kumar, P., Rawat, S. (eds) Distributed Computing and Intelligent Technology. ICDCIT 2023. Lecture Notes in Computer Science, vol 13776. Springer, Cham. https://doi.org/10.1007/978-3-031-24848-1_6

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  • DOI: https://doi.org/10.1007/978-3-031-24848-1_6

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