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Almost Optimal Algorithms for Token Collision in Anonymous Networks

Authors Sirui Bai, Xinyu Fu , Xudong Wu, Penghui Yao , Chaodong Zheng

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  • Theory of computation → Distributed algorithms
Keywords
  • Token collision
  • anonymous networks
  • deterministic algorithms

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Abstract

In distributed systems, situations often arise where some nodes each holds a collection of tokens, and all nodes collectively need to determine whether all tokens are distinct. For example, if each token represents a logged-in user, the problem corresponds to checking whether there are duplicate logins. Similarly, if each token represents a data object or a timestamp, the problem corresponds to checking whether there are conflicting operations in distributed databases. In distributed computing theory, unique identifiers generation is also related to this problem: each node generates one token, which is its identifier, then a verification phase is needed to ensure that all identifiers are unique.
In this paper, we formalize and initiate the study of token collision. In this problem, a collection of k tokens, each represented by some length-L bit string, are distributed to n nodes of an anonymous CONGEST network in an arbitrary manner. The nodes need to determine whether there are tokens with an identical value. We present near optimal deterministic algorithms for the token collision problem with Õ(D+k⋅L/log n) round complexity, where D denotes the network diameter. Besides high efficiency, the prior knowledge required by our algorithms is also limited. For completeness, we further present a near optimal randomized algorithm for token collision.

Cite As Get BibTex

Sirui Bai, Xinyu Fu, Xudong Wu, Penghui Yao, and Chaodong Zheng. Almost Optimal Algorithms for Token Collision in Anonymous Networks. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.4

Author Details

Sirui Bai
  • State Key Laboratory for Novel Software Technology, Nanjing University, China
Xinyu Fu
  • State Key Laboratory for Novel Software Technology, Nanjing University, China
Xudong Wu
  • State Key Laboratory for Novel Software Technology, Nanjing University, China
Penghui Yao
  • State Key Laboratory for Novel Software Technology, Nanjing University, China
  • Hefei National Laboratory, China
Chaodong Zheng
  • State Key Laboratory for Novel Software Technology, Nanjing University, China

Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 62332009, 62172207, 12347104), the Department of Science and Technology of Jiangsu Province of China (Grant No. BK20211148) and Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302901).

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