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Memory and communication efficient algorithm for decentralized counting of nodes in networks.

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This study introduces a novel deterministic algorithm for distributed graph size estimation. The algorithm enables each node in a connected network to calculate the total number of nodes efficiently, given an upper bound.

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Area of Science:

  • Distributed Systems
  • Graph Theory
  • Network Algorithms

Background:

  • Distributed graph size estimation faces theoretical limitations.
  • Existing solutions include stochastic and naive deterministic algorithms.
  • Real-world applications like collective robotics require accurate graph size calculation.

Purpose of the Study:

  • To present a deterministic and distributed algorithm for graph size calculation.
  • To enable every node in a connected graph to determine its size in finite time.
  • To provide a solution that is efficient in terms of memory, communication, and time complexity.

Main Methods:

  • The algorithm relies on iterative information aggregation in local hubs.
  • Information is then broadcast throughout the entire graph.
  • Requires an initial upper bound on the graph size.

Main Results:

  • The proposed algorithm allows deterministic distributed node counting.
  • It is more efficient in average node memory and communication cost compared to previous deterministic methods.
  • Average-case time complexity is comparable or better than existing deterministic approaches.

Conclusions:

  • The presented algorithm offers an efficient solution for distributed graph size estimation.
  • It has broader applicability to problems like graph summation and quorum sensing.
  • This method advances distributed computing and network analysis.