Efficient Computation in Congested Anonymous Dynamic Networks
An anonymous dynamic network is a network of indistinguishable processes whose communication links may appear or disappear unpredictably over time. Previous research has shown that deterministically computing an arbitrary function of a multiset of input values given to these processes takes only a linear number of communication rounds (Di Luna-Viglietta, FOCS 2022).
However, fast algorithms for anonymous dynamic networks rely on the construction and transmission of large data structures called history trees, whose size is polynomial in the number of processes. This approach is unfeasible if the network is congested, and only messages of logarithmic size can be sent through its links. Observe that sending a large message piece by piece over several rounds is not in itself a solution, due to the anonymity of the processes combined with the dynamic nature of the network. Moreover, it is known that certain basic tasks such as all-to-all token dissemination (by means of single-token forwarding) require Ω(n²/log n) rounds in congested networks (Dutta et al., SODA 2013).
In this work, we develop a series of practical and efficient techniques that make it possible to use history trees in congested anonymous dynamic networks. Among other applications, we show how to compute arbitrary functions in such networks in O(n³) communication rounds, greatly improving upon previous state-of-the-art algorithms for congested networks.
anonymous dynamic network
congested network
history tree
Theory of computation~Distributed algorithms
Computing methodologies~Distributed algorithms
49:1-49:19
Regular Paper
Giuseppe A. Di Luna was Giovanni Viglietta was
https://arxiv.org/abs/2301.07849
Giuseppe A.
Di Luna
Giuseppe A. Di Luna
DIAG, Sapienza University of Rome, Italy
partially supported by Sapienza Progetto Ateneo RM1221816C1760BF.
Giovanni
Viglietta
Giovanni Viglietta
Department of Computer Science and Engineering, University of Aizu, Japan
partially supported by the JSPS KAKENHI grant 23K10985.
10.4230/LIPIcs.MFCS.2024.49
D. Angluin, J. Aspnes, and D. Eisenstat. Fast Computation by Population Protocols with a Leader. Distributed Computing, 21(3):61-75, 2008.
J. Aspnes, J. Beauquier, J. Burman, and D. Sohier. Time and Space Optimal Counting in Population Protocols. In Proceedings of the 20th International Conference on Principles of Distributed Systems (OPODIS '16), pages 13:1-13:17, 2016.
J. Beauquier, J. Burman, S. Clavière, and D. Sohier. Space-Optimal Counting in Population Protocols. In Proceedings of the 29th International Symposium on Distributed Computing (DISC '15), pages 631-646, 2015.
J. Beauquier, J. Burman, and S. Kutten. A Self-stabilizing Transformer for Population Protocols with Covering. Theoretical Computer Science, 412(33):4247-4259, 2011.
D. P. Bertsekas and J. N. Tsitsiklis. Parallel and Distributed Computation: Numerical Methods. Prentice-Hall, Inc., USA, 1989.
A. Casteigts, F. Flocchini, B. Mans, and N. Santoro. Shortest, Fastest, and Foremost Broadcast in Dynamic Networks. International Journal of Foundations of Computer Science, 26(4):499-522, 2015.
A. Casteigts, P. Flocchini, W. Quattrociocchi, and N. Santoro. Time-Varying Graphs and Dynamic Networks. International Journal of Parallel, Emergent and Distributed Systems, 27(5):387-408, 2012.
B. Charron-Bost and P. Lambein-Monette. Randomization and Quantization for Average Consensus. In Proceedings of the 57th IEEE Conference on Decision and Control (CDC '18), pages 3716-3721, 2018.
B. Charron-Bost and P. Lambein-Monette. Computing Outside the Box: Average Consensus over Dynamic Networks. In Proceedings of the 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND '22), pages 10:1-10:16, 2022.
B. Chazelle. The Total s-Energy of a Multiagent System. SIAM Journal on Control and Optimization, 49(4):1680-1706, 2011.
G. A. Di Luna and G. Baldoni. Brief Announcement: Investigating the Cost of Anonymity on Dynamic Networks. In Proceedings of the 34th ACM Symposium on Principles of Distributed Computing (PODC '15), pages 339-341, 2015.
G. A. Di Luna, R. Baldoni, S. Bonomi, and I. Chatzigiannakis. Counting in Anonymous Dynamic Networks Under Worst-Case Adversary. In Proceedings of the 34th IEEE International Conference on Distributed Computing Systems (ICDCS '14), pages 338-347, 2014.
G. A. Di Luna, S. Bonomi, I. Chatzigiannakis, and R. Baldoni. Counting in Anonymous Dynamic Networks: An Experimental Perspective. In Proceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS '13), pages 139-154, 2013.
G. A. Di Luna, P. Flocchini, T. Izumi, T. Izumi, N. Santoro, and G. Viglietta. Population Protocols with Faulty Interactions: The Impact of a Leader. Theoretical Computer Science, 754:35-49, 2019.
G. A. Di Luna and G. Viglietta. Computing in Anonymous Dynamic Networks Is Linear. In Proceedings of the 63rd IEEE Symposium on Foundations of Computer Science (FOCS '22), pages 1122-1133, 2022.
G. A. Di Luna and G. Viglietta. Brief Announcement: Efficient Computation in Congested Anonymous Dynamic Networks. In Proceedings of the 42nd ACM Symposium on Principles of Distributed Computing (PODC '23), pages 176-179, 2023.
G. A. Di Luna and G. Viglietta. Optimal computation in leaderless and multi-leader disconnected anonymous dynamic networks. In Proceedings of the 37th International Symposium on Distributed Computing (DISC '23), pages 18:1-18:20, 2023.
C. Dutta, G. Pandurangan, R. Rajaraman, Z. Sun, and E. Viola. On the Complexity of Information Spreading in Dynamic Networks. In Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '13), pages 717-736, 2013.
P. Fraigniaud, A. Pelc, D. Peleg, and S. Pérennes. Assigning Labels in Unknown Anonymous Networks. In Proceedings of the 19th ACM Symposium on Principles of Distributed Computing (PODC '00), pages 101-111, 2000.
B. Haeupler and F. Kuhn. Lower Bounds on Information Dissemination in Dynamic Networks. In Proceedings of the 26th International Symposium on Distributed Computing (DISC '12), pages 166-180, 2012.
D. R. Kowalski and M. A. Mosteiro. Polynomial Counting in Anonymous Dynamic Networks with Applications to Anonymous Dynamic Algebraic Computations. In Proceedings of the 45th International Colloquium on Automata, Languages, and Programming (ICALP '18), pages 156:1-156:14, 2018.
D. R. Kowalski and M. A. Mosteiro. Polynomial Anonymous Dynamic Distributed Computing Without a Unique Leader. In Proceedings of the 46th International Colloquium on Automata, Languages, and Programming (ICALP '19), pages 147:1-147:15, 2019.
D. R. Kowalski and M. A. Mosteiro. Polynomial Counting in Anonymous Dynamic Networks with Applications to Anonymous Dynamic Algebraic Computations. Journal of the ACM, 67(2):11:1-11:17, 2020.
D. R. Kowalski and M. A. Mosteiro. Supervised Average Consensus in Anonymous Dynamic Networks. In Proceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA '21), pages 307-317, 2021.
D. R. Kowalski and M. A. Mosteiro. Efficient Distributed Computations in Anonymous Dynamic Congested Systems with Opportunistic Connectivity. arXiv:2202.07167 [cs.DC], pages 1-28, 2022.
D. R. Kowalski and M. A. Mosteiro. Polynomial Anonymous Dynamic Distributed Computing Without a Unique Leader. Journal of Computer and System Sciences, 123:37-63, 2022.
F. Kuhn, T. Locher, and R. Oshman. Gradient Clock Synchronization in Dynamic Networks. Theory of Computing Systems, 49(4):781-816, 2011.
F. Kuhn, N. Lynch, and R. Oshman. Distributed Computation in Dynamic Networks. In Proceedings of the 42nd ACM Symposium on Theory of Computing (STOC '10), pages 513-522, 2010.
F. Kuhn, Y. Moses, and R. Oshman. Coordinated Consensus in Dynamic Networks. In Proceedings of the 30th ACM Symposium on Principles of Distributed Computing (PODC '11), pages 1-10, 2011.
F. Kuhn and R. Oshman. Dynamic Networks: Models and Algorithms. SIGACT News, 42(1):82-96, 2011.
O. Michail, I. Chatzigiannakis, and P. G. Spirakis. Naming and Counting in Anonymous Unknown Dynamic Networks. In Proceedings of the 15th International Symposium on Stabilizing, Safety, and Security of Distributed Systems (SSS '13), pages 281-295, 2013.
O. Michail and P. G. Spirakis. Elements of the Theory of Dynamic Networks. Communications of the ACM, 61(2):72, 2018.
A. Nedić, A. Olshevsky, A. E. Ozdaglar, and J. N. Tsitsiklis. On Distributed Averaging Algorithms and Quantization Effects. IEEE Transactions on Automatic Control, 54(11):2506-2517, 2009.
R. O'Dell and R. Wattenhofer. Information Dissemination in Highly Dynamic Graphs. In Proceedings of the 5th Joint Workshop on Foundations of Mobile Computing (DIALM-POMC '05), pages 104-110, 2005.
A. Olshevsky. Linear Time Average Consensus and Distributed Optimization on Fixed Graphs. SIAM Journal on Control and Optimization, 55(6):3990-4014, 2017.
A. Olshevsky and J. N. Tsitsiklis. Convergence Speed in Distributed Consensus and Averaging. SIAM Journal on Control and Optimization, 48(1):33-55, 2009.
A. Olshevsky and J. N. Tsitsiklis. A Lower Bound for Distributed Averaging Algorithms on the Line Graph. IEEE Transactions on Automatic Control, 56(11):2694-2698, 2011.
D. Peleg. Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics, USA, 2000.
N. Sakamoto. Comparison of Initial Conditions for Distributed Algorithms on Anonymous Networks. In Proceedings of the 18th ACM Symposium on Principles of Distributed Computing (PODC '99), pages 173-179, 1999.
T. Sharma and M. Bashir. Use of Apps in the COVID-19 Response and the Loss of Privacy Protection. Nature Medicine, 26(8):1165-1167, 2020.
J. N. Tsitsiklis. Problems in Decentralized Decision Making and Computation. PhD thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1984.
M. Yamashita and T. Kameda. Computing on Anonymous Networks. I. Characterizing the Solvable Cases. IEEE Transactions on Parallel and Distributed Systems, 7(1):69-89, 1996.
Y. Yuan, G.-B. Stan, L. Shi, M. Barahona, and J. Goncalves. Decentralised Minimum-Time Consensus. Automatica, 49(5):1227-1235, 2013.
Giuseppe A. Di Luna and Giovanni Viglietta
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