Beeping a Deterministic Time-Optimal Leader Election
The beeping model is an extremely restrictive broadcast communication model that relies only on carrier sensing. In this model, we solve the leader election problem with an asymptotically optimal round complexity of O(D + log n), for a network of unknown size n and unknown diameter D (but with unique identifiers). Contrary to the best previously known algorithms in the same setting, the proposed one is deterministic. The techniques we introduce give a new insight as to how local constraints on the exchangeable messages can result in efficient algorithms, when dealing with the beeping model.
Using this deterministic leader election algorithm, we obtain a randomized leader election algorithm for anonymous networks with an asymptotically optimal round complexity of O(D + log n) w.h.p. In previous works this complexity was obtained in expectation only.
Moreover, using deterministic leader election, we obtain efficient algorithms for symmetry-breaking and communication procedures: O(log n) time MIS and 5-coloring for tree networks (which is time-optimal), as well as k-source multi-broadcast for general graphs in O(min(k,log n) * D + k log{(n M)/k}) rounds (for messages in {1,..., M}). This latter result improves on previous solutions when the number of sources k is sublogarithmic (k = o(log n)).
distributed algorithms
leader election
beeping model
time complexity
deterministic algorithms
wireless networks
Theory of computation~Distributed computing models
Theory of computation~Distributed algorithms
Theory of computation~Design and analysis of algorithms
20:1-20:17
Regular Paper
A full version is available at https://hal.archives-ouvertes.fr/hal-01794711.
Fabien
Dufoulon
Fabien Dufoulon
LRI, Université Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France
https://orcid.org/0000-0003-2977-4109
Janna
Burman
Janna Burman
LRI, Université Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France
Joffroy
Beauquier
Joffroy Beauquier
LRI, Université Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France
10.4230/LIPIcs.DISC.2018.20
Y. Afek, N. Alon, Z. Bar-Joseph, A. Cornejo, B. Haeupler, and F. Kuhn. Beeping a maximal independent set. Distributed Computing, 26(4):195-208, Aug 2013.
D. Alistarh, A. Cornejo, M. Ghaffari, and N. Lynch. Firefly synchronization with asynchronous wake-up. In Workshop on Biological Distributed Algorithms, 2014.
J. Beauquier, J. Burman, F. Dufoulon, and S. Kutten. Fast Beeping Protocols for Deterministic MIS and (Δ+1)-Coloring in Sparse Graphs. In IEEE INFOCOM, 2018, to appear.
A. Casteigts, Y. Métivier, J. M. Robson, and A. Zemmari. Design Patterns in Beeping Algorithms. In OPODIS, pages 15:1-15:16, 2016.
A. Casteigts, Y. Métivier, J.M. Robson, and A. Zemmari. Deterministic leader election in 𝒪(D+ logn) time with messages of size 𝒪(1). In DISC, pages 16-28, 2016.
I. Chlamtac and S. Kutten. On broadcasting in radio networks - problem analysis and protocol design. IEEE Transactions on Communications, 33(12):1240-1246, 1985.
A. Cornejo and F. Kuhn. Deploying wireless networks with beeps. In DISC, pages 148-162, 2010.
A. Czumaj and P. Davies. Optimal leader election in multi-hop radio networks. ArXiv e-prints, 2015. URL: http://arxiv.org/abs/1505.06149.
http://arxiv.org/abs/1505.06149
A. Czumaj and P. Davies. Brief announcement: Optimal leader election in multi-hop radio networks. In PODC, pages 47-49, 2016.
A. Czumaj and P. Davies. Communicating with Beeps. In OPODIS, pages 1-16, 2016.
Y. Dinitz and N. Solomon. Two absolute bounds for distributed bit complexity. In Structural Information and Communication Complexity, pages 115-126, 2005.
K.-T. Förster, J. Seidel, and R. Wattenhofer. Deterministic leader election in multi-hop beeping networks. In DISC, pages 212-226, 2014.
M. Ghaffari and B. Haeupler. Near optimal leader election in multi-hop radio networks. In SODA, pages 748-766, 2013.
S. Gilbert and C. Newport. The computational power of beeps. In DISC, pages 31-46, 2015.
R. Guerraoui and A. Maurer. Byzantine fireflies. In DISC, pages 47-59, 2015.
S. Kutten, G. Pandurangan, D. Peleg, P. Robinson, and A. Trehan. On the complexity of universal leader election. In PODC, pages 100-109, 2013.
Y. Métivier, J.M. Robson, and A. Zemmari. Analysis of fully distributed splitting and naming probabilistic procedures and applications. Theoretical Computer Science, 584:115-130, 2015. Special Issue on Structural Information and Communication Complexity.
K. Nakano and S. Olariu. Randomized o(log log n)-round leader election protocols in packet radio networks. In Algorithms and Computation, pages 210-219, 1998.
S. Navlakha and Z. Bar-Joseph. Distributed information processing in biological and computational systems. Commun. ACM, 58(1):94-102, 2014.
D. Peleg. Time-efficient broadcasting in radio networks: A review. In Distributed Computing and Internet Technology, pages 1-18, Berlin, Heidelberg, 2007. Springer Berlin Heidelberg.
J. Schneider and R. Wattenhofer. What is the use of collision detection (in wireless networks)? In DISC, pages 133-147, 2010.
A. Scott, P. Jeavons, and L. Xu. Feedback from nature: An optimal distributed algorithm for maximal independent set selection. In PODC, pages 147-156, 2013.
J. Seidel. Anonymous distributed computing: computability, randomization and checkability. PhD thesis, ETH Zurich, Zürich, Switzerland, 2015. URL: http://d-nb.info/1080812695.
http://d-nb.info/1080812695
Fabien Dufoulon, Janna Burman, and Joffroy Beauquier
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode