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We give a maximal independent set (MIS) algorithm that runs in $O(\log \log \Delta)$ rounds in the congested clique model, where $\Delta$ is the maximum degree of the input graph.
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Lotker, Z., Pavlov, E., Patt-Shamir, B., Peleg, D.: Mst construction in o(log log n) communication rounds. In: Proceedings of the Fifteenth Annual ACM Symposium on Parallel Algorithms and Architectures. pp. 94–100. SPAA ’03, ACM, New York, NY, USA (2003), http://doi.acm.org/10.1145/777412.777428
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Kuhn, F., Moscibroda, T., Wattenhofer, R.: What cannot be computed locally! In: Proceedings of the Twenty-third Annual ACM Symposium on Principles of Distributed Computing. pp. 300–309. PODC ’04, ACM, New York, NY, USA (2004), http://doi.acm.org/10.1145/1011767.1011811
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Lotker, Z., Patt-Shamir, B., Pavlov, E., Peleg, D.: Minimum-weight spanning tree construction in o(log log n) communication rounds. SIAM J. Comput. 35(1), 120–131 (Jul 2005), https://doi.org/10.1137/S0097539704441848
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Fanghänel, A., Kesselheim, T., Vöcking, B.: Improved algorithms for latency minimization in wireless networks. Theor. Comput. Sci. 412(24), 2657–2667 (May 2011), http://dx.doi.org/10.1016/j.tcs.2010.05.004
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Lenzen, C.: Optimal deterministic routing and sorting on the congested clique. In: Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing. pp. 42–50. PODC ’13, ACM, New York, NY, USA (2013), http://doi.acm.org/10.1145/2484239.2501983
2013
Cited alongside, same era.
Drucker, A., Kuhn, F., Oshman, R.: On the power of the congested clique model. In: Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing. pp. 367–376. PODC ’14, ACM, New York, NY, USA (2014), http://doi.acm.org/10.1145/2611462.2611493
2014
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Hegeman, J.W., Pemmaraju, S.V.: Lessons from the congested clique applied to mapreduce. In: Halldórsson, M.M. (ed.) Structural Information and Communication Complexity. pp. 149–164. Springer International Publishing, Cham (2014)
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Hegeman, J.W., Pemmaraju, S.V., Sardeshmukh, V.B.: Near-constant-time distributed algorithms on a congested clique. In: Kuhn, F. (ed.) Distributed Computing. pp. 514–530. Springer Berlin Heidelberg, Berlin, Heidelberg (2014)
Ghaffari, M.: An improved distributed algorithm for maximal independent set. In: Proceedings of the Twenty-seventh Annual ACM-SIAM Symposium on Discrete Algorithms. pp. 270–277. SODA ’16, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2016), http://dl.acm.org/citation.cfm?id=2884435.2884455
2016
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Ghaffari, M., Parter, M.: Mst in log-star rounds of congested clique. In: Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing. pp. 19–28. PODC ’16, ACM, New York, NY, USA (2016), http://doi.acm.org/10.1145/2933057.2933103
2016
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Kuhn, F., Moscibroda, T., Wattenhofer, R.: Local computation: Lower and upper bounds. J. ACM 63(2), 17:1–17:44 (Mar 2016), http://doi.acm.org/10.1145/2742012
2016
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Le Gall, F.: Further algebraic algorithms in the congested clique model and applications to graph-theoretic problems. In: Gavoille, C., Ilcinkas, D. (eds.) Distributed Computing. pp. 57–70. Springer Berlin Heidelberg, Berlin, Heidelberg (2016)
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2014
Cited alongside, same era.
Ahn, K.J., Cormode, G., Guha, S., McGregor, A., Wirth, A.: Correlation clustering in data streams. In: Proceedings of the 32Nd International Conference on International Conference on Machine Learning - Volume 37. pp. 2237–2246. ICML’15, JMLR.org (2015), http://dl.acm.org/citation.cfm?id=3045118.3045356
2015
Cited alongside, same era.
Censor-Hillel, K., Kaski, P., Korhonen, J.H., Lenzen, C., Paz, A., Suomela, J.: Algebraic methods in the congested clique. In: Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing. pp. 143–152. PODC ’15, ACM, New York, NY, USA (2015), http://doi.acm.org/10.1145/2767386.2767414
2015
Cited alongside, same era.
Hegeman, J.W., Pandurangan, G., Pemmaraju, S.V., Sardeshmukh, V.B., Scquizzato, M.: Toward optimal bounds in the congested clique: Graph connectivity and mst. In: Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing. pp. 91–100. PODC ’15, ACM, New York, NY, USA (2015), http://doi.acm.org/10.1145/2767386.2767434
2015
Cited alongside, same era.
Barenboim, L., Elkin, M., Pettie, S., Schneider, J.: The locality of distributed symmetry breaking. J. ACM 63(3), 20:1–20:45 (Jun 2016), http://doi.acm.org/10.1145/2903137
2016
Cited alongside, same era.
2016
Later among the works it cites.
Ghaffari, M.: Distributed mis via all-to-all communication. In: Proceedings of the ACM Symposium on Principles of Distributed Computing. pp. 141–149. PODC ’17, ACM, New York, NY, USA (2017), http://doi.acm.org/10.1145/3087801.3087830
2017
Later among the works it cites.
Korhonen, J.H., Suomela, J.: Brief announcement: Towards a complexity theory for the congested clique. In: 31st International Symposium on Distributed Computing, DISC 2017, October 16-20, 2017, Vienna, Austria. pp. 55:1–55:3 (2017), https://doi.org/10.4230/LIPIcs.DISC.2017.55
2017
Later among the works it cites.
Jurdzinski, T., Nowicki, K.: MST in O (1) rounds of congested clique. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, LA, USA, January 7-10, 2018. pp. 2620–2632 (2018), https://doi.org/10.1137/1.9781611975031.167
2018
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