{"title":"Linear-Size hopsets with small hopbound, and constant-hopbound hopsets in RNC","authors":"Michael Elkin, Ofer Neiman","doi":"10.1007/s00446-022-00431-z","DOIUrl":"https://doi.org/10.1007/s00446-022-00431-z","url":null,"abstract":"<p>Hopsets are a fundamental graph-theoretic and graph-algorithmic construct, and they are widely used for distance-related problems in a variety of computational settings. Currently existing constructions of hopsets produce hopsets either with <span>(Omega (n log n))</span> edges, or with a hopbound <span>(n^{Omega (1)})</span>. In this paper we devise a construction of <i>linear-size</i> hopsets with hopbound (ignoring the dependence on <span>(epsilon )</span>) <span>((log log n)^{log log n + O(1)})</span>. This improves the previous hopbound for linear-size hopsets almost <i>exponentially</i>. We also devise efficient implementations of our construction in PRAM and distributed settings. The only existing PRAM algorithm [19] for computing hopsets with a constant (i.e., independent of <i>n</i>) hopbound requires <span>(n^{Omega (1)})</span> time. We devise a PRAM algorithm with polylogarithmic running time for computing hopsets with a constant hopbound, i.e., our running time is <i>exponentially</i> better than the previous one. Moreover, these hopsets are also significantly sparser than their counterparts from [19]. We apply these hopsets to achieve the following online variant of shortest paths in the PRAM model: preprocess a given weighted graph within polylogarithmic time, and then given any query vertex <i>v</i>, report all approximate shortest paths from <i>v</i> in <i>constant time</i>. All previous constructions of hopsets require either polylogarithmic time per query or polynomial preprocessing time.</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"20 10","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507820","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":"Near-optimal distributed dominating set in bounded arboricity graphs","authors":"Michal Dory, M. Ghaffari, S. Ilchi","doi":"10.1145/3519270.3538437","DOIUrl":"https://doi.org/10.1145/3519270.3538437","url":null,"abstract":"We describe a simple deterministic $$O( varepsilon ^{-1} log Delta )$$ O ( ε - 1 log Δ ) round distributed algorithm for $$(2alpha +1)(1 + varepsilon )$$ ( 2 α + 1 ) ( 1 + ε ) approximation of minimum weighted dominating set on graphs with arboricity at most $$alpha $$ α . Here $$Delta $$ Δ denotes the maximum degree. We also show a lower bound proving that this round complexity is nearly optimal even for the unweighted case, via a reduction from the celebrated KMW lower bound on distributed vertex cover approximation (Kuhn et al. in JACM 63:116, 2016). Our algorithm improves on all the previous results (that work only for unweighted graphs) including a randomized $$O(alpha ^2)$$ O ( α 2 ) approximation in $$O(log n)$$ O ( log n ) rounds (Lenzen et al. in International symposium on distributed computing, Springer, 2010), a deterministic $$O(alpha log Delta )$$ O ( α log Δ ) approximation in $$O(log Delta )$$ O ( log Δ ) rounds (Lenzen et al. in international symposium on distributed computing, Springer, 2010), a deterministic $$O(alpha )$$ O ( α ) approximation in $$O(log ^2 Delta )$$ O ( log 2 Δ ) rounds (implicit in Bansal et al. in Inform Process Lett 122:21–24, 2017; Proceeding 17th symposium on discrete algorithms (SODA), 2006), and a randomized $$O(alpha )$$ O ( α ) approximation in $$O(alpha log n)$$ O ( α log n ) rounds (Morgan et al. in 35th International symposiumon distributed computing, 2021). We also provide a randomized $$O(alpha log Delta )$$ O ( α log Δ ) round distributed algorithm that sharpens the approximation factor to $$alpha (1+o(1))$$ α ( 1 + o ( 1 ) ) . If each node is restricted to do polynomial-time computations, our approximation factor is tight in the first order as it is NP-hard to achieve $$alpha - 1 - varepsilon $$ α - 1 - ε approximation (Bansal et al. in Inform Process Lett 122:21-24, 2017).","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"1 1","pages":"1-12"},"PeriodicalIF":1.3,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47763316","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":"Posterior chamber phakic intraocular lens implantation after laser in situ keratomileusis.","authors":"Kazutaka Kamiya, Kimiya Shimizu, Akihito Igarashi, Yoshihiro Kitazawa, Takashi Kojima, Tomoaki Nakamura, Kazuo Ichikawa, Sachiko Fukuoka, Kahoko Fujimoto","doi":"10.1186/s40662-022-00282-6","DOIUrl":"10.1186/s40662-022-00282-6","url":null,"abstract":"<p><strong>Background: </strong>To assess the multicenter outcomes of posterior chamber phakic intraocular lens implantation with a central hole (EVO-ICL, STAAR Surgical) for patients undergoing previous laser in situ keratomileusis (LASIK).</p><p><strong>Methods: </strong>This case series enrolled 31 eyes of 21 consecutive patients undergoing EVO-ICL implantation to correct residual refractive errors after LASIK at 7 nationwide major surgical sites. We investigated safety, efficacy, predictability, stability, and adverse events at 1 week, 1, 3, and 6 months postoperatively, and at the final visit.</p><p><strong>Results: </strong>The mean observation period was 1.6 ± 1.8 years. Uncorrected and corrected visual acuities were - 0.14 ± 0.11 and - 0.22 ± 0.09 logMAR at 6 months postoperatively. At 6 months postoperatively, 81% and 100% of eyes were within ± 0.5 D and ± 1.0 D, respectively, of the targeted correction. We found neither significant manifest refraction changes of 0.05 ± 0.38 D from 1 week to 6 months nor apparent intraoperative or postoperative complications in any case.</p><p><strong>Conclusions: </strong>Our multicenter study confirmed that the EVO-ICL provided good outcomes in safety, efficacy, predictability, and stability, even in post-LASIK eyes. Therefore, EVO-ICL implantation may be a viable surgical option, even for correcting residual refractive errors after LASIK. Trial registration University Hospital Medical Information Network Clinical Trial Registry (000045295).</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"1 1","pages":"15"},"PeriodicalIF":4.1,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9008970/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89832009","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":"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}