[{"isi":1,"publisher":"Association for Computing Machinery","status":"public","department":[{"_id":"DaAl"}],"quality_controlled":"1","publication":"Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing","page":"481–491","date_created":"2021-08-17T18:11:16Z","month":"07","acknowledgement":"This work is partially supported by a Weizmann-UK Making Connections Grant, the Centre for Discrete Mathematics and its Applications (DIMAP), IBM Faculty Award, EPSRC award EP/V01305X/1, European Research Council (ERC) Grant No. 949083, the Minerva foundation with funding from the Federal German Ministry for Education and Research No. 713238, and the European Union’s Horizon 2020 programme under the Marie Skłodowska-Curie grant agreement No 754411.","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"doi":"10.1145/3465084.3467903","language":[{"iso":"eng"}],"conference":{"location":"Virtual, Italy","name":"PODC: Principles of Distributed Computing","start_date":"2021-07-26","end_date":"2021-07-30"},"title":"Component stability in low-space massively parallel computation","ec_funded":1,"citation":{"short":"A. Czumaj, P. Davies, M. Parter, in:, Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2021, pp. 481–491.","ama":"Czumaj A, Davies P, Parter M. Component stability in low-space massively parallel computation. In: <i>Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2021:481–491. doi:<a href=\"https://doi.org/10.1145/3465084.3467903\">10.1145/3465084.3467903</a>","apa":"Czumaj, A., Davies, P., &#38; Parter, M. (2021). Component stability in low-space massively parallel computation. In <i>Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing</i> (pp. 481–491). Virtual, Italy: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3465084.3467903\">https://doi.org/10.1145/3465084.3467903</a>","chicago":"Czumaj, Artur, Peter Davies, and Merav Parter. “Component Stability in Low-Space Massively Parallel Computation.” In <i>Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing</i>, 481–491. Association for Computing Machinery, 2021. <a href=\"https://doi.org/10.1145/3465084.3467903\">https://doi.org/10.1145/3465084.3467903</a>.","ista":"Czumaj A, Davies P, Parter M. 2021. Component stability in low-space massively parallel computation. Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing. PODC: Principles of Distributed Computing, 481–491.","ieee":"A. Czumaj, P. Davies, and M. Parter, “Component stability in low-space massively parallel computation,” in <i>Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing</i>, Virtual, Italy, 2021, pp. 481–491.","mla":"Czumaj, Artur, et al. “Component Stability in Low-Space Massively Parallel Computation.” <i>Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing</i>, Association for Computing Machinery, 2021, pp. 481–491, doi:<a href=\"https://doi.org/10.1145/3465084.3467903\">10.1145/3465084.3467903</a>."},"author":[{"last_name":"Czumaj","first_name":"Artur","full_name":"Czumaj, Artur"},{"full_name":"Davies, Peter","first_name":"Peter","last_name":"Davies","orcid":"0000-0002-5646-9524","id":"11396234-BB50-11E9-B24C-90FCE5697425"},{"first_name":"Merav","full_name":"Parter, Merav","last_name":"Parter"}],"type":"conference","day":"21","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2106.01880"}],"oa":1,"publication_status":"published","article_processing_charge":"No","arxiv":1,"abstract":[{"text":"In this paper, we study the power and limitations of component-stable algorithms in the low-space model of Massively Parallel Computation (MPC). Recently Ghaffari, Kuhn and Uitto (FOCS 2019) introduced the class of component-stable low-space MPC algorithms, which are, informally, defined as algorithms for which the outputs reported by the nodes in different connected components are required to be independent. This very natural notion was introduced to capture most (if not all) of the known efficient MPC algorithms to date, and it was the first general class of MPC algorithms for which one can show non-trivial conditional lower bounds. In this paper we enhance the framework of component-stable algorithms and investigate its effect on the complexity of randomized and deterministic low-space MPC. Our key contributions include: 1) We revise and formalize the lifting approach of Ghaffari, Kuhn and Uitto. This requires a very delicate amendment of the notion of component stability, which allows us to fill in gaps in the earlier arguments. 2) We also extend the framework to obtain conditional lower bounds for deterministic algorithms and fine-grained lower bounds that depend on the maximum degree Δ. 3) We demonstrate a collection of natural graph problems for which non-component-stable algorithms break the conditional lower bound obtained for component-stable algorithms. This implies that, for both deterministic and randomized algorithms, component-stable algorithms are conditionally weaker than the non-component-stable ones.\r\n\r\nAltogether our results imply that component-stability might limit the computational power of the low-space MPC model, paving the way for improved upper bounds that escape the conditional lower bound setting of Ghaffari, Kuhn, and Uitto.","lang":"eng"}],"_id":"9933","date_published":"2021-07-21T00:00:00Z","publication_identifier":{"isbn":["9781450385480"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_updated":"2023-08-17T07:11:32Z","external_id":{"isi":["000744439800049"],"arxiv":["2106.01880"]},"oa_version":"Submitted Version","year":"2021"},{"month":"07","abstract":[{"text":"There has recently been a surge of interest in the computational and complexity properties of the population model, which assumes n anonymous, computationally-bounded nodes, interacting at random, with the goal of jointly computing global predicates. Significant work has gone towards investigating majority or consensus dynamics in this model: that is, assuming that every node is initially in one of two states X or Y, determine which state had higher initial count.\r\n\r\nIn this paper, we consider a natural generalization of majority/consensus, which we call comparison : in its simplest formulation, we are given two baseline states, X and Y, present in any initial configuration in fixed, but possibly small counts. One of these states has higher count than the other: we will assume |X_0| > C |Y_0| for some constant C > 1. The challenge is to design a protocol by which nodes can quickly and reliably decide on which of the baseline states X_0 and Y_0 has higher initial count. We begin by analyzing a simple and general dynamics solving the above comparison problem, which uses O( log n ) states per node, and converges in O(log n) (parallel) time, with high probability, to a state where the whole population votes on opinions X or Y at rates proportional to the initial concentrations of |X_0| vs. |Y_0|. We then describe how this procedure can be bootstrapped to solve comparison, i.e. have every node in the population reach the \"correct'' decision, with probability 1 - o(1), at the cost of O (log log n) additional states. Further, we prove that this dynamics is self-stabilizing, in the sense that it converges to the correct decision from arbitrary initial states, and leak-robust, in the sense that it can withstand spurious faulty reactions, which are known to occur in practical implementations of population protocols. Our analysis is based on a new martingale concentration result relating the discrete-time evolution of a population protocol to its expected (steady-state) analysis, which should be a useful tool when analyzing opinion dynamics and epidemic dissemination in the population model.","lang":"eng"}],"_id":"9951","date_created":"2021-08-22T22:01:20Z","date_published":"2021-07-21T00:00:00Z","page":"55-65","article_processing_charge":"No","publication":"Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing","department":[{"_id":"DaAl"}],"quality_controlled":"1","status":"public","publication_status":"published","publisher":"Association for Computing Machinery","isi":1,"day":"21","type":"conference","author":[{"id":"4A899BFC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3650-940X","last_name":"Alistarh","first_name":"Dan-Adrian","full_name":"Alistarh, Dan-Adrian"},{"id":"4B865388-F248-11E8-B48F-1D18A9856A87","last_name":"Töpfer","full_name":"Töpfer, Martin","first_name":"Martin"},{"first_name":"Przemysław","full_name":"Uznański, Przemysław","last_name":"Uznański"}],"year":"2021","oa_version":"None","citation":{"mla":"Alistarh, Dan-Adrian, et al. “Comparison Dynamics in Population Protocols.” <i>Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing</i>, Association for Computing Machinery, 2021, pp. 55–65, doi:<a href=\"https://doi.org/10.1145/3465084.3467915\">10.1145/3465084.3467915</a>.","ista":"Alistarh D-A, Töpfer M, Uznański P. 2021. Comparison dynamics in population protocols. Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing, 55–65.","ieee":"D.-A. Alistarh, M. Töpfer, and P. Uznański, “Comparison dynamics in population protocols,” in <i>Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing</i>, Virtual, Italy, 2021, pp. 55–65.","chicago":"Alistarh, Dan-Adrian, Martin Töpfer, and Przemysław Uznański. “Comparison Dynamics in Population Protocols.” In <i>Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing</i>, 55–65. Association for Computing Machinery, 2021. <a href=\"https://doi.org/10.1145/3465084.3467915\">https://doi.org/10.1145/3465084.3467915</a>.","apa":"Alistarh, D.-A., Töpfer, M., &#38; Uznański, P. (2021). Comparison dynamics in population protocols. In <i>Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing</i> (pp. 55–65). Virtual, Italy: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3465084.3467915\">https://doi.org/10.1145/3465084.3467915</a>","ama":"Alistarh D-A, Töpfer M, Uznański P. Comparison dynamics in population protocols. In: <i>Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2021:55-65. doi:<a href=\"https://doi.org/10.1145/3465084.3467915\">10.1145/3465084.3467915</a>","short":"D.-A. Alistarh, M. Töpfer, P. Uznański, in:, Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2021, pp. 55–65."},"title":"Comparison dynamics in population protocols","conference":{"name":"PODC: Symposium on Principles of Distributed Computing","start_date":"2021-07-26","end_date":"2021-07-30","location":"Virtual, Italy"},"external_id":{"isi":["000744439800005"]},"scopus_import":"1","language":[{"iso":"eng"}],"date_updated":"2023-08-11T10:56:04Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"isbn":["9781450385480"]},"doi":"10.1145/3465084.3467915","acknowledgement":"We would like to thank Rati Gelashvili for very useful discussions, and the PODC anonymous reviewers for their careful reading of our paper, and for their useful remarks. This work is partially supported by the Polish National Science Center (NCN) grant UMO2017/25/B/ST6/02010."}]