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Upper Bounds on Graph Diameter Based on Laplacian Eigenvalues for Stopping Distributed Flooding Algorithm

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Part of the Lecture Notes in Networks and Systems book series (LNNS,volume 722)


Data aggregation is essential in many modern wireless sensor network-based applications as its usage can guarantee a significant increase in the Quality of Service in this technology. In this paper, we consider a geographically deployed group of synchronous wireless sensor nodes employing the distributed flooding algorithm for data aggregation of sensor-measured values. As previously identified in many other papers, properly bounded algorithms are crucial for wireless sensor networks’ effective and long-lasting operation. Therefore, we apply four upper bounds on the graph diameter based on Laplacian eigenvalues to stop executing the mentioned algorithm in the synchronous mode. The purpose of this paper is to provide a comparative study of these four stopping criteria in random graphs of various connectivity and graph order in order to identify the best-performing approach in terms of the number of iterations required for the algorithm to be completed. Moreover, the performance of these approaches is compared to the optimal solution for stopping the distributed flooding algorithm in the synchronous mode, i.e., bounding the algorithm based on the exact value of the graph diameter. Thus, the main contribution of this paper is to analyze the potential applicability of the examined upper bounds to stopping the mentioned concerned algorithm and identify its optimal stopping criterion based on the Laplacian spectrum for real-world scenarios.


  • Data aggregation
  • Distributed algorithms
  • Flooding algorithm
  • Graph diameter
  • Laplacian eigenvalues
  • Stopping criterion
  • Synchronous mode
  • Upper bounds
  • Wireless sensor networks

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This work was supported by the Slovak Scientific Grand Agency VEGA under the contract 2/0135/23 “Intelligent sensor systems and data processing” and by the Slovak Research and Development Agency under the contract No. APVV-19-0220.

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Correspondence to Martin Kenyeres .

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Kenyeres, M., Kenyeres, J. (2023). Upper Bounds on Graph Diameter Based on Laplacian Eigenvalues for Stopping Distributed Flooding Algorithm. In: Silhavy, R., Silhavy, P. (eds) Software Engineering Research in System Science. CSOC 2023. Lecture Notes in Networks and Systems, vol 722. Springer, Cham.

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