Approximate Neighbor Counting in Radio Networks

Authors Calvin Newport, Chaodong Zheng

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Calvin Newport
  • Georgetown University, Washington, D.C., United States
Chaodong Zheng
  • State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China

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Calvin Newport and Chaodong Zheng. Approximate Neighbor Counting in Radio Networks. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


For many distributed algorithms, neighborhood size is an important parameter. In radio networks, however, obtaining this information can be difficult due to ad hoc deployments and communication that occurs on a collision-prone shared channel. This paper conducts a comprehensive survey of the approximate neighbor counting problem, which requires nodes to obtain a constant factor approximation of the size of their network neighborhood. We produce new lower and upper bounds for three main variations of this problem in the radio network model: (a) the network is single-hop and every node must obtain an estimate of its neighborhood size; (b) the network is multi-hop and only a designated node must obtain an estimate of its neighborhood size; and (c) the network is multi-hop and every node must obtain an estimate of its neighborhood size. In studying these problem variations, we consider solutions with and without collision detection, and with both constant and high success probability. Some of our results are extensions of existing strategies, while others require technical innovations. We argue this collection of results provides insight into the nature of this well-motivated problem (including how it differs from related symmetry breaking tasks in radio networks), and provides a useful toolbox for algorithm designers tackling higher level problems that might benefit from neighborhood size estimates.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Radio networks
  • neighborhood size estimation
  • approximate counting


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  1. Reuven Bar-Yehuda, Oded Goldreich, and Alon Itai. On the Time-complexity of Broadcast in Radio Networks: An Exponential Gap Between Determinism and Randomization. In Proceedings of the 6th Annual ACM Symposium on Principles of Distributed Computing, PODC '87, pages 98-108. ACM, 1987. Google Scholar
  2. Jacir Luiz Bordim, JiangTao Cui, Tatsuya Hayashi, Koji Nakano, and Stephan Olariu. Energy-Efficient Initialization Protocols for Ad-hoc Radio Networks. In International Symposium on Algorithms and Computation, ISAAC '99, pages 215-224. Springer, 1999. Google Scholar
  3. Philipp Brandes, Marcin Kardas, Marek Klonowski, Dominik Pajak, and Roger Wattenhofer. Fast Size Approximation of a Radio Network in Beeping Model. Theoretical Computer Science, In Press, 2017. URL:
  4. Ioannis Caragiannis, Clemente Galdi, and Christos Kaklamanis. Basic Computations in Wireless Networks. In International Symposium on Algorithms and Computation, ISAAC '05, pages 533-542. Springer, 2005. Google Scholar
  5. Binbin Chen, Ziling Zhou, and Haifeng Yu. Understanding RFID Counting Protocols. In Proceedings of the 19th Annual International Conference on Mobile Computing and Networking, MobiCom '13, pages 291-302. ACM, 2013. Google Scholar
  6. Israel Cidon and Moshe Sidi. Conflict Multiplicity Estimation and Batch Resolution Algorithms. IEEE Transactions on Information Theory, 34(1):101-110, 1988. Google Scholar
  7. Alejandro Cornejo and Fabian Kuhn. Deploying Wireless Networks with Beeps. In International Symposium on Distributed Computing, DISC '10, pages 148-162. Springer, 2010. Google Scholar
  8. Mohsen Ghaffari, Nancy Lynch, and Srikanth Sastry. Leader Election Using Loneliness Detection. Distributed Computing, 25(6):427-450, 2012. Google Scholar
  9. Seth Gilbert, Valerie King, Seth Pettie, Ely Porat, Jared Saia, and Maxwell Young. (Near) Optimal Resource-competitive Broadcast with Jamming. In Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA '14, pages 257-266. ACM, 2014. Google Scholar
  10. Seth Gilbert, Fabian Kuhn, and Chaodong Zheng. Communication Primitives in Cognitive Radio Networks. In Proceedings of the 2017 ACM Symposium on Principles of Distributed Computing, PODC '17, pages 23-32. ACM, 2017. Google Scholar
  11. Albert G. Greenberg, Philippe Flajolet, and Richard E. Ladner. Estimating the Multiplicities of Conflicts to Speed Their Resolution in Multiple Access Channels. Journal of the ACM, 34(2):289-325, 1987. Google Scholar
  12. Tomasz Jurdziński, Mirosław Kutyłowski, and Jan Zatopiański. Energy-Efficient Size Approximation of Radio Networks with No Collision Detection. In International Computing and Combinatorics Conference, COCOON '02, pages 279-289. Springer, 2002. Google Scholar
  13. Tomasz Jurdzinski and Grzegorz Stachowiak. Probabilistic Algorithms for the Wake-Up Problem in Single-Hop Radio Networks. Theory of Computing Systems, 38(3):347-367, 2005. Google Scholar
  14. Jedrzej Kabarowski, Mirosław Kutyłowski, and Wojciech Rutkowski. Adversary Immune Size Approximation of Single-Hop Radio Networks. In International Conference on Theory and Applications of Models of Computation, pages 148-158. Springer, 2006. Google Scholar
  15. Marek Klonowski and Kamil Wolny. Immune Size Approximation Algorithms in Ad Hoc Radio Network. In European Conference on Wireless Sensor Networks, pages 33-48. Springer, 2012. Google Scholar
  16. Michael Luby. A Simple Parallel Algorithm for the Maximal Independent Set Problem. In Proceedings of the 17th Annual ACM Symposium on Theory of Computing, STOC '85, pages 1-10. ACM, 1985. Google Scholar
  17. Michael Mitzenmacher and Eli Upfal. Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, 2005. Google Scholar
  18. Koji Nakan and Stephan Olari. Uniform Leader Election Protocols for Radio Networks. IEEE Transactions on Parallel and Distributed Systems, 13(5):516-526, 2002. Google Scholar
  19. Calvin Newport. Radio Network Lower Bounds Made Easy. In Proceedings of the 28th International Symposium on Distributed Computing, DISC '14, pages 258-272. Springer, 2014. Google Scholar
  20. Calvin Newport and Chaodong Zheng. Approximate Neighbor Counting in Radio Networks, 2018. URL:
  21. Muhammad Shahzad and Alex X. Liu. Every Bit Counts: Fast and Scalable RFID Estimation. In Proceedings of the 18th Annual International Conference on Mobile Computing and Networking, MobiCom '12, pages 365-376. ACM, 2012. Google Scholar
  22. Dan E. Willard. Log-logarithmic Selection Resolution Protocols in a Multiple Access Channel. SIAM Journal on Computing, 15(2):468-477, 1986. Google Scholar
  23. Yuanqing Zheng and Mo Li. ZOE: Fast cardinality estimation for large-scale RFID systems. In Proceedings of the 32nd IEEE International Conference on Computer Communications, INFOCOM '13, pages 908-916. IEEE, 2013. Google Scholar
  24. Yuanqing Zheng, Mo Li, and Chen Qian. PET: Probabilistic Estimating Tree for Large-Scale RFID Estimation. In Proceedings of the 31st International Conference on Distributed Computing Systems, ICDCS '11, pages 37-46. IEEE, 2011. Google Scholar
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