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Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice

Authors Pawel Garncarek , Tomasz Jurdzinski , Dariusz R. Kowalski , Shay Kutten , Miguel A. Mosteiro

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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Radio Networks
  • Local Broadcast
  • Distributed Deterministic Algorithms
  • Lower Bounds
  • Graph algorithms
  • Advice
  • Labeling Schemes
  • Local Domination

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Abstract

Radio Networks (RN) is one of the fundamental models for network communication where nodes can broadcast messages locally but their simultaneous transmissions can interfere with each other at their shared neighbors. This work focuses on performing the very fundamental primitive of Local Broadcast, in spite of the interferences.
We investigate to what extent local knowledge, called advice, relating to the 2-local domination number γ₂ may speed up Local Broadcast. Specifically for each node and some dominating set, knowledge about some neighboring dominating node and the local number among the neighbors of that dominating node. We show that such advice is sufficient to build an efficient oblivious transmission schedule. Along those lines, we present three algorithms trading the level of adaptiveness (from oblivious to adaptive) for bits of advice per node (from O(log (Δγ₂)) to 1). All our algorithms complete Local Broadcast in Õ(Δγ₂²) rounds, where Δ is the maximum degree of the network. 
On the side of lower bounds, we show that, for each quasi-adaptive deterministic Local Broadcast algorithm, there is some RN that requires Ω(min{(min{Δ,γ₂}/log n)²,n}) communication rounds, where n is the number of network nodes. In quasi-adaptive protocols nodes may stop executing once its computational task is completed. To the best of our knowledge, this is the first (nearly) quadratic Local Broadcast (same message for all neighbors) lower bound in the RN model. Our lower bound is stronger than previous works in multiple ways: i) it is nearly quadratically better than the best known general lower bound for this class of algorithms, ii) it applies to a wider class of algorithms than previous work for fully oblivious, iii) it achieves similar time lower bound than previous work proved for a much more demanding Local Broadcast where each node sends a possibly different message to each neighbor, and iv) it takes into account the local domination parameter γ₂.

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Pawel Garncarek, Tomasz Jurdzinski, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro. Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ISAAC.2025.34

Author Details

Pawel Garncarek
  • Institute of Computer Science, University of Wrocław, Poland
Tomasz Jurdzinski
  • Institute of Computer Science, University of Wrocław, Poland
Dariusz R. Kowalski
  • School of Computer and Cyber Sciences, Augusta University, GA, USA
Shay Kutten
  • Department of Data and Decision Sciences and the Grand Technion Energy Program, Technion, Haifa, Israel
Miguel A. Mosteiro
  • Computer Science Department, Pace University, New York, NY, USA

Funding

  • Garncarek, Pawel: Supported by the National Science Center, Poland (NCN), grant 35 2020/39/B/ST6/03288.
  • Jurdzinski, Tomasz: Supported by the National Science Center, Poland (NCN), grant 35 2020/39/B/ ST6/03288.
  • Kutten, Shay: The work of this author was funded in part by grant 1346/22 from the Israeli Science 37 Foundation. His research was carried out within the framework of the Grand Technion Energy 38 Program (GTEP). A part of this work was done while with the Fraunhofer Darmstadt.
  • Mosteiro, Miguel A.: Partially supported by Pace SRC grant and Kenan Fund.

References

  1. Norman Abramson. The aloha system: Another alternative for computer communications. In Proceedings of the November 17-19, 1970, fall joint computer conference, pages 281-285, 1970. URL: https://doi.org/10.1145/1478462.1478502.
  2. Noga Alon, Amotz Bar-Noy, Nathan Linial, and David Peleg. A lower bound for radio broadcast. Journal of Computer and System Sciences, 43(2):290-298, 1991. URL: https://doi.org/10.1016/0022-0000(91)90015-W.
  3. Reuven Bar-Yehuda, Oded Goldreich, and Alon Itai. On the time-complexity of broadcast in multi-hop radio networks: An exponential gap between determinism and randomization. Journal of Computer and System Sciences, 45(1):104-126, 1992. URL: https://doi.org/10.1016/0022-0000(92)90042-H.
  4. Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. Optimal two-stage algorithms for group testing problems. SIAM J. Comput., 34(5):1253-1270, 2005. URL: https://doi.org/10.1137/S0097539703428002.
  5. Joan Boyar, Lene M Favrholdt, Christian Kudahl, Kim S Larsen, and Jesper W Mikkelsen. Online algorithms with advice: A survey. ACM Computing Surveys (CSUR), 50(2):1-34, 2017. URL: https://doi.org/10.1145/3056461.
  6. Gewu Bu, Maria Potop-Butucaru, and Mikaël Rabie. Wireless broadcast with short labels. In International Conference on Networked Systems, pages 146-169. Springer, 2020. URL: https://doi.org/10.1007/978-3-030-67087-0_10.
  7. J. Capetanakis. Tree algorithms for packet broadcast channels. IEEE Trans. Inf. Theor., 25(5):505-515, September 1979. URL: https://doi.org/10.1109/TIT.1979.1056093.
  8. Mahdi Cheraghchi and Vasileios Nakos. Combinatorial group testing and sparse recovery schemes with near-optimal decoding time. In Sandy Irani, editor, 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS'20 2020, Durham, NC, USA, November 16-19, 2020, pages 1203-1213. IEEE, 2020. URL: https://doi.org/10.1109/FOCS46700.2020.00115.
  9. Imrich Chlamtac and Shay Kutten. On broadcasting in radio networks-problem analysis and protocol design. IEEE Transactions on Communications, 33(12):1240-1246, 1985. URL: https://doi.org/10.1109/TCOM.1985.1096245.
  10. Bogdan S. Chlebus and Dariusz R. Kowalski. Almost optimal explicit selectors. In Maciej Liskiewicz and Rüdiger Reischuk, editors, Fundamentals of Computation Theory, 15th International Symposium, FCT 2005, Lübeck, Germany, August 17-20, 2005, Proceedings, volume 3623 of Lecture Notes in Computer Science, pages 270-280. Springer, 2005. URL: https://doi.org/10.1007/11537311_24.
  11. Israel Cidon and Osnat Mokryn. Propagation and leader election in a multihop broadcast environment. In Distributed Computing: 12th International Symposium, DISC’98 Andros, Greece, September 24-26, 1998 Proceedings 12, pages 104-118. Springer, 1998. URL: https://doi.org/10.1007/BFB0056477.
  12. Andrea EF Clementi, Angelo Monti, and Riccardo Silvestri. Selective families, superimposed codes, and broadcasting on unknown radio networks. In Proceedings of the twelfth annual ACM-SIAM Symposium on Discrete algorithms (SODA'01), pages 709-718, 2001. Google Scholar
  13. Andrea E.F. Clementi, Angelo Monti, and Riccardo Silvestri. Distributed broadcast in radio networks of unknown topology. Theoretical Computer Science, 302(1):337-364, 2003. URL: https://doi.org/10.1016/S0304-3975(02)00851-4.
  14. Peter Davies. Optimal message-passing with noisy beeps. In Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing (PODC'23), pages 300-309, 2023. URL: https://doi.org/10.1145/3583668.3594594.
  15. Peter Davies. Uniting general-graph and geometric-based radio networks via independence number parametrization. In Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing (PODC'23), pages 290-299, 2023. URL: https://doi.org/10.1145/3583668.3594595.
  16. Anders Dessmark and Andrzej Pelc. Broadcasting in geometric radio networks. Journal of Discrete Algorithms, 5(1):187-201, 2007. URL: https://doi.org/10.1016/J.JDA.2006.07.001.
  17. Krzysztof Diks, Evangelos Kranakis, Danny Krizanc, and Andrzej Pelc. The impact of information on broadcasting time in linear radio networks. Theoretical Computer Science, 287(2):449-471, 2002. URL: https://doi.org/10.1016/S0304-3975(01)00256-0.
  18. Faith Ellen and Seth Gilbert. Constant-length labelling schemes for faster deterministic radio broadcast. In Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA'20), pages 213-222, 2020. URL: https://doi.org/10.1145/3350755.3400238.
  19. Faith Ellen, Barun Gorain, Avery Miller, and Andrzej Pelc. Constant-length labeling schemes for deterministic radio broadcast. ACM Transactions on Parallel Computing, 8(3):1-17, 2021. URL: https://doi.org/10.1145/3470633.
  20. Paul Erdős, Peter Frankl, and Zoltán Füredi. Families of finite sets in which no set is covered by the union of r others. Israel J. Math, 51(1-2):79-89, 1985. Google Scholar
  21. Ralph J. Faudree, Zdeněk Ryjáček, and Richard H. Schelp. On local and global independence numbers of a graph. Discrete Applied Mathematics, 132(1):79-84, 2003. Stability in Graphs and Related Topics. URL: https://doi.org/10.1016/S0166-218X(03)00391-3.
  22. Pierre Fraigniaud, David Ilcinkas, and Andrzej Pelc. Communication algorithms with advice. J. Comput. Syst. Sci., 76(3-4):222-232, 2010. URL: https://doi.org/10.1016/J.JCSS.2009.07.002.
  23. Adam Gańczorz, Tomasz Jurdziński, and Andrzej Pelc. Optimal-length labeling schemes for fast deterministic communication in radio networks. arXiv preprint arXiv:2410.07382, 2024. Google Scholar
  24. Cyril Gavoille, David Peleg, Stéphane Pérennes, and Ran Raz. Distance labeling in graphs. Journal of algorithms, 53(1):85-112, 2004. URL: https://doi.org/10.1016/J.JALGOR.2004.05.002.
  25. Mohsen Ghaffari and Bernhard Haeupler. Near optimal leader election in multi-hop radio networks. In Proceedings of the twenty-fourth annual ACM-SIAM Symposium on Discrete algorithms (SODA'13), pages 748-766. SIAM, 2013. URL: https://doi.org/10.1137/1.9781611973105.54.
  26. Seth Gilbert, Nancy A. Lynch, Calvin Newport, and Dominik Pajak. On simple back-off in unreliable radio networks. Theor. Comput. Sci., 806:489-508, 2020. URL: https://doi.org/10.1016/J.TCS.2019.08.027.
  27. Christian Glacet, Avery Miller, and Andrzej Pelc. Time vs. information tradeoffs for leader election in anonymous trees. ACM Trans. Algorithms, 13(3):31:1-31:41, 2017. URL: https://doi.org/10.1145/3039870.
  28. Barun Gorain and Andrzej Pelc. Finding the size of a radio network with short labels. In Proceedings of the 19th International Conference on Distributed Computing and Networking, pages 1-10, 2018. URL: https://doi.org/10.1145/3154273.3154298.
  29. Barun Gorain and Andrzej Pelc. Finding the size and the diameter of a radio network using short labels. Theoretical Computer Science, 864:20-33, 2021. URL: https://doi.org/10.1016/J.TCS.2021.02.004.
  30. Albert G. Greenberg and Shmuel Winograd. A lower bound on the time needed in the worst case to resolve conflicts deterministically in multiple access channels. J. ACM, 32(3):589-596, 1985. URL: https://doi.org/10.1145/3828.214125.
  31. J.F. Hayes. An adaptive technique for local distribution. IEEE Communications Magazine, 19(2), 1981. Google Scholar
  32. Michael A. Henning. Distance Domination in Graphs, pages 205-250. Springer International Publishing, Cham, 2020. URL: https://doi.org/10.1007/978-3-030-51117-3_7.
  33. David Ilcinkas, Dariusz R Kowalski, and Andrzej Pelc. Fast radio broadcasting with advice. Theoretical Computer Science, 411(14-15):1544-1557, 2010. URL: https://doi.org/10.1016/J.TCS.2010.01.004.
  34. Michal Katz, Nir A Katz, Amos Korman, and David Peleg. Labeling schemes for flow and connectivity. SIAM Journal on Computing, 34(1):23-40, 2004. URL: https://doi.org/10.1137/S0097539703433912.
  35. William Kautz and Roy Singleton. Nonrandom binary superimposed codes. IEEE Transactions on Information Theory, 10(4):363-377, 1964. URL: https://doi.org/10.1109/TIT.1964.1053689.
  36. Janos Komlós and Albert Greenberg. An asymptotically nonadaptive algorithm for conflict resolution in multiple-access channels. IEEE Transactions on Information Theory, 31:302-306, April 1985. URL: https://doi.org/10.1109/TIT.1985.1057020.
  37. Amos Korman, Shay Kutten, and David Peleg. Proof labeling schemes. In Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing, pages 9-18, 2005. URL: https://doi.org/10.1145/1073814.1073817.
  38. Dariusz R. Kowalski. On selection problem in radio networks. In Proceedings of the Twenty-fourth Annual ACM Symposium on Principles of Distributed Computing, PODC '05, pages 158-166, New York, NY, USA, 2005. ACM. URL: https://doi.org/10.1145/1073814.1073843.
  39. Eyal Kushilevitz and Yishay Mansour. An ω(d$$1log(n/d)) lower bound for broadcast in radio networks. SIAM journal on Computing, 27(3):702-712, 1998. Google Scholar
  40. Nancy Lynch and Calvin Newport. A (truly) local broadcast layer for unreliable radio networks. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing (PODC'15), pages 109-118, 2015. URL: https://doi.org/10.1145/2767386.2767411.
  41. Robert Metcalfe and David R. Boggs. Ethernet: Distributed packet switching for local computer networks. Commun. ACM, 19(7):395-404, 1976. URL: https://doi.org/10.1145/360248.360253.
  42. David Peleg. Distributed computing: a locality-sensitive approach. SIAM, Philadelphia, PA, USA, 2000. Google Scholar
  43. David Peleg. Time-efficient broadcasting in radio networks: A review. In Tomasz Janowski and Hrushikesha Mohanty, editors, Distributed Computing and Internet Technology, 4th International Conference, ICDCIT 2007, Bangalore, India, December 17-20, Proceedings, volume 4882 of Lecture Notes in Computer Science, pages 1-18. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-77115-9_1.
  44. B S. Tsybakov and V A. Mikhailov. Free synchronous packet access in broadcast channel with feedback. Probl Inf Transm, 14(4), October 1978. Google Scholar
  45. Mikkel Thorup and Uri Zwick. Approximate distance oracles. Journal of the ACM (JACM), 52(1):1-24, 2005. URL: https://doi.org/10.1145/1044731.1044732.
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