{"title":"Revisiting asynchronous fault tolerant computation with optimal resilience","authors":"Ittai Abraham, Danny Dolev, Gilad Stern","doi":"10.1007/s00446-021-00416-4","DOIUrl":"https://doi.org/10.1007/s00446-021-00416-4","url":null,"abstract":"<p>The celebrated result of Fischer, Lynch and Paterson is the fundamental lower bound for asynchronous fault tolerant computation: any 1-crash resilient asynchronous agreement protocol must have some (possibly measure zero) probability of not terminating. In 1994, Ben-Or, Kelmer and Rabin published a <i>proof-sketch</i> of a lesser known lower bound for asynchronous fault tolerant computation with optimal resilience in face of a Byzantine adversary: if <span>(nle 4t)</span> then any t-resilient asynchronous verifiable secret sharing protocol must have some <b>non-zero</b> probability of not terminating. Our main contribution is to revisit this lower bound and provide a rigorous and more general proof. Our second contribution is to show how to avoid this lower bound. We provide a protocol with optimal resilience that is almost surely terminating for a <i>strong common coin</i> functionality. Using this new primitive we provide an almost surely terminating protocol with optimal resilience for asynchronous Byzantine agreement that has a new <i>fair validity</i> property. To the best of our knowledge this is the first asynchronous Byzantine agreement with fair validity in the information theoretic setting.\u0000</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"34 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Guerraoui, P. Kuznetsov, M. Monti, M. Pavlovic, Dragos-Adrian Seredinschi
{"title":"Correction to: The consensus number of a cryptocurrency","authors":"R. Guerraoui, P. Kuznetsov, M. Monti, M. Pavlovic, Dragos-Adrian Seredinschi","doi":"10.1007/s00446-022-00422-0","DOIUrl":"https://doi.org/10.1007/s00446-022-00422-0","url":null,"abstract":"","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"35 1","pages":"17"},"PeriodicalIF":1.3,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41830087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Distributed ComputingPub Date : 2022-01-01Epub Date: 2022-01-20DOI: 10.1007/s00446-021-00418-2
Danupon Nanongkai, Michele Scquizzato
{"title":"Equivalence classes and conditional hardness in massively parallel computations.","authors":"Danupon Nanongkai, Michele Scquizzato","doi":"10.1007/s00446-021-00418-2","DOIUrl":"10.1007/s00446-021-00418-2","url":null,"abstract":"<p><p>The <i>Massively Parallel Computation</i> (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of classical graph problems. So far, the only way to argue lower bounds for this model is to condition on conjectures about the hardness of some specific problems, such as graph connectivity on promise graphs that are either one cycle or two cycles, usually called the <i>one cycle versus two cycles</i> problem. This is unlike the traditional arguments based on conjectures about complexity classes (e.g., <math><mrow><mi>P</mi> <mo>≠</mo> <mi>NP</mi></mrow> </math> ), which are often more robust in the sense that refuting them would lead to groundbreaking algorithms for a whole bunch of problems. In this paper we present connections between problems and classes of problems that allow the latter type of arguments. These connections concern the class of problems solvable in a sublogarithmic amount of rounds in the MPC model, denoted by <math><mrow><mi>MPC</mi> <mo>(</mo> <mi>o</mi> <mo>(</mo> <mo>log</mo> <mi>N</mi> <mo>)</mo> <mo>)</mo></mrow> </math> , and the standard space complexity classes <math><mi>L</mi></math> and <math><mi>NL</mi></math> , and suggest conjectures that are robust in the sense that refuting them would lead to many surprisingly fast new algorithms in the MPC model. We also obtain new conditional lower bounds, and prove new reductions and equivalences between problems in the MPC model. Specifically, our main results are as follows.Lower bounds conditioned on the one cycle versus two cycles conjecture can be instead argued under the <math><mrow><mi>L</mi> <mo>⊈</mo> <mi>MPC</mi> <mo>(</mo> <mi>o</mi> <mo>(</mo> <mo>log</mo> <mi>N</mi> <mo>)</mo> <mo>)</mo></mrow> </math> conjecture: these two assumptions are equivalent, and refuting either of them would lead to <math><mrow><mi>o</mi> <mo>(</mo> <mo>log</mo> <mi>N</mi> <mo>)</mo></mrow> </math> -round MPC algorithms for a large number of challenging problems, including list ranking, minimum cut, and planarity testing. In fact, we show that these problems and many others require asymptotically the same number of rounds as the seemingly much easier problem of distinguishing between a graph being one cycle or two cycles.Many lower bounds previously argued under the one cycle versus two cycles conjecture can be argued under an even more robust (thus harder to refute) conjecture, namely <math><mrow><mi>NL</mi> <mo>⊈</mo> <mi>MPC</mi> <mo>(</mo> <mi>o</mi> <mo>(</mo> <mo>log</mo> <mi>N</mi> <mo>)</mo> <mo>)</mo></mrow> </math> . Refuting this conjecture would lead to <math><mrow><mi>o</mi> <mo>(</mo> <mo>log</mo> <mi>N</mi> <mo>)</mo></mrow> </math> -round MPC algorithms for an even larger set of problems, including all-pairs shortest paths, betweenness centrality, and all aforementioned ones. Lower bounds under this conjecture hold for probl","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"35 1","pages":"165-183"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8907129/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44815276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Distributed computation and reconfiguration in actively dynamic networks","authors":"O. Michail, George Skretas, P. Spirakis","doi":"10.1007/s00446-021-00415-5","DOIUrl":"https://doi.org/10.1007/s00446-021-00415-5","url":null,"abstract":"","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"35 1","pages":"185 - 206"},"PeriodicalIF":1.3,"publicationDate":"2021-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42469584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sublinear-time distributed algorithms for detecting small cliques and even cycles","authors":"T. Eden, N. Fiat, O. Fischer, F. Kuhn, R. Oshman","doi":"10.1007/s00446-021-00409-3","DOIUrl":"https://doi.org/10.1007/s00446-021-00409-3","url":null,"abstract":"","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"35 1","pages":"207 - 234"},"PeriodicalIF":1.3,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43043251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Distributed bare-bones communication in wireless networks","authors":"Bogdan S. Chlebus, D. Kowalski, Shailesh Vaya","doi":"10.1007/s00446-021-00413-7","DOIUrl":"https://doi.org/10.1007/s00446-021-00413-7","url":null,"abstract":"","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"35 1","pages":"59 - 80"},"PeriodicalIF":1.3,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47930717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}