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Wait-free approximate agreement on graphs [article]

Dan Alistarh and Faith Ellen and Joel Rybicki
<span title="2021-03-16">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We also extend the reduction from 2-set agreement to a larger class of graphs, showing that approximate agreement on on these graphs is unsolvable.  ...  Approximate agreement is one of the few variants of consensus that can be solved in a wait-free manner in asynchronous systems where processes communicate by reading and writing to shared memory.  ...  Sk lodowska-Curie grant agreement No. 840605 and from the Natural Science and Engineering Research Council of Canada grant RGPIN-2020-04178.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2103.08949v1">arXiv:2103.08949v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fk73bmoennb3tpvnjep66sj5la">fatcat:fk73bmoennb3tpvnjep66sj5la</a> </span>
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Brief Announcement: Variants of Approximate Agreement on Graphs and Simplicial Complexes

Jérémy Ledent
<span title="2021-07-21">2021</span> <i title="ACM"> Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing </i> &nbsp;
We focus on two variants of approximate agreement on graphs, edge agreement and clique agreement.  ...  Many variants of this task have been considered in the literature: continuous or discrete ones; multi-dimensional ones; as well as agreement on graphs and other spaces.  ...  ACKNOWLEDGMENTS The author would like to thank Éric Goubault and Sergio Rajsbaum for helpful discussions on this topic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/3465084.3467946">doi:10.1145/3465084.3467946</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xureio3cvjaxpd2iny7ch2jtgy">fatcat:xureio3cvjaxpd2iny7ch2jtgy</a> </span>
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Fault-Tolerant Consensus in Directed Graphs

Lewis Tseng, Nitin H. Vaidya
<span title="">2015</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t5fzg7fyy5byfdcl2vrzbn43ty" style="color: black;">Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing - PODC &#39;15</a> </i> &nbsp;
Other prior work on directed graphs has explored somewhat different problems than those solved in this paper.  ...  systems, • Approximate crash-tolerant consensus in asynchronous systems, and • Exact Byzantine consensus in synchronous systems.  ...  Our prior work [23, 24] has considered a restricted class of iterative algorithms for achieving approximate Byzantine consensus in directed graphs, where fault-free nodes must agree on values that are  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2767386.2767399">doi:10.1145/2767386.2767399</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/podc/TsengV15.html">dblp:conf/podc/TsengV15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m635r4vva5f6rdhrtsu7gf6gdi">fatcat:m635r4vva5f6rdhrtsu7gf6gdi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200320054606/http://disc.ece.illinois.edu/publications/2015/fault%20tolerant%20consensus%20in%20directed%20graphs/lewis_podc15.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cc/b6/ccb66aedd955e1d29782e7c079d45c55ec73d123.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2767386.2767399"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Byzantine Approximate Agreement on Graphs

Thomas Nowak, Joel Rybicki, Michael Wagner
<span title="2019-10-11">2019</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2pcluxp32rfojgwekdrryxoaqu" style="color: black;">International Symposium on Distributed Computing</a> </i> &nbsp;
In the approximate agreement task, each processor i receives an input value xi and has to decide on an output value yi such that 1. the output values are in the convex hull of the non-faulty processors  ...  In addition, we give the first Byzantine-tolerant algorithm for a variant of lattice agreement.  ...  agreement on graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.disc.2019.29">doi:10.4230/lipics.disc.2019.29</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/wdag/NowakR19.html">dblp:conf/wdag/NowakR19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pgsdcxsj3fb27px2p45ecgqmkq">fatcat:pgsdcxsj3fb27px2p45ecgqmkq</a> </span>
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Two Convergence Problems for Robots on Graphs

Armando Castaneda, Sergio Rajsbaum, Matthieu Roy
<span title="">2016</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cuxyw5lz7bfjlhk4czk3m4wciq" style="color: black;">2016 Seventh Latin-American Symposium on Dependable Computing (LADC)</a> </i> &nbsp;
In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge.  ...  We consider also a variant of robot convergence on graphs, edge covering, where additionally it is required that not all robots end up on the same vertex.  ...  approximate agreement theorem of topology.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ladc.2016.21">doi:10.1109/ladc.2016.21</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ladc/CastanedaRR16.html">dblp:conf/ladc/CastanedaRR16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sluro6ohsrdxhhw4for263c6gq">fatcat:sluro6ohsrdxhhw4for263c6gq</a> </span>
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The decidability of distributed decision tasks (extended abstract)

Maurice Herlihy, Sergio Rajsbaum
<span title="">1997</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC &#39;97</a> </i> &nbsp;
In either case, basic agreement has a wait-free read/write protocol. 8.2.2 Link Agreement Just as for basic agreement, we argue by reduction to a graph problem.  ...  Since dim(SO U SI ) z 1, basic graph agreement has a wait-free read/write protocol, If k >1, the protocol is illustrated in Figure 6 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/258533.258652">doi:10.1145/258533.258652</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stoc/HerlihyR97.html">dblp:conf/stoc/HerlihyR97</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/riroqeazgbeznjf525hf6acozm">fatcat:riroqeazgbeznjf525hf6acozm</a> </span>
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Byzantine Approximate Agreement on Graphs [article]

Thomas Nowak, Joel Rybicki
<span title="2019-11-19">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In the approximate agreement task, each processor i receives an input value x_i and has to decide on an output value y_i such that - the output values are in the convex hull of the non-faulty processors  ...  In addition, we give the first Byzantine-tolerant algorithm for a variant of lattice agreement.  ...  Byzantine approximate agreement on chordal graphs. We give algorithms for approximate agreement on trees and chordal graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1908.02743v2">arXiv:1908.02743v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gcphdcy3uvfu5ccqvsxk77ey2u">fatcat:gcphdcy3uvfu5ccqvsxk77ey2u</a> </span>
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Page 6444 of Mathematical Reviews Vol. , Issue 2004h [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The paper shows that each loop agreement (i.e. a family of wait- free tasks including instances of set agreement and approximate agreement tasks) can be assigned an algebraic signature consisting  ...  The slowdown of a step-by-step part of the simulation is O(logm).” 2004h:68041 68Q10 68M14 Herlihy, Maurice (1-BRN-C; Providence, RI); Rajsbaum, Sergio (MEX-NAM-IM; México) A classification of wait-free  ... 
<span class="external-identifiers"> </span>
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Convergence and covering on graphs for wait-free robots

Armando Castañeda, Sergio Rajsbaum, Matthieu Roy
<span title="2018-01-08">2018</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vct5ya6gxbcelemee3tlxkwmiu" style="color: black;">Journal of the Brazilian Computer Society</a> </i> &nbsp;
In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge.  ...  We consider also a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex.  ...  approximate agreement theorem of topology.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/s13173-017-0065-8">doi:10.1186/s13173-017-0065-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eeqrt6pt2rclnpel3omd5aa23e">fatcat:eeqrt6pt2rclnpel3omd5aa23e</a> </span>
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Crash-Tolerant Consensus in Directed Graphs [article]

Lewis Tseng, Nitin Vaidya
<span title="2015-01-02">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This work considers a point-to-point network of n nodes connected by directed links, and proves tight necessary and sufficient conditions on the underlying communication graphs for achieving consensus  ...  node must be some node's input. • Termination: every fault-free node eventually decides on an output.  ...  Condition WAIT: Denote by reach i (F ) the set of nodes that have paths to node i in the reduced graph G F .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1412.8532v2">arXiv:1412.8532v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/auk5hvhjfbfqvjk7fgxadqjzga">fatcat:auk5hvhjfbfqvjk7fgxadqjzga</a> </span>
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Computing in the Presence of Concurrent Solo Executions [chapter]

Maurice Herlihy, Sergio Rajsbaum, Michel Raynal, Julien Stainer
<span title="">2014</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The paper studies also the relation linking d-set agreement and (d, ǫ)-solo approximate agreement in asynchronous wait-free message-passing systems.  ...  It also introduces the (d, ǫ)-solo approximate agreement task, which generalizes ǫ-approximate agreement, and proves that (d, ǫ)-solo approximate agreement can be solved in the d-solo model, but cannot  ...  This provides us with a better insight on a bound on the "maximal partitioning" allowed to solve (d − 1, ǫ)-solo approximate agreement in the wait-free message-passing model.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-54423-1_19">doi:10.1007/978-3-642-54423-1_19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i6u2egcc3ncmjijvdnqbubpllu">fatcat:i6u2egcc3ncmjijvdnqbubpllu</a> </span>
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Foreword: Parallelism in Algorithms and Architectures

Geppino Pucci, Victor Luchangco, Rajmohan Rajaraman
<span title="2014-01-08">2014</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qj6jzeossfhihfshwf7nb7lbcq" style="color: black;">Theory of Computing Systems</a> </i> &nbsp;
but unrealistic system assumptions, and then shows how to adapt this technique to produce a practical wait-free concurrent object implementations that perform well on real machines (though with weaker  ...  The second paper Highly-Efficient Wait-Free Synchronization, by Panagiota Fatourou and Nikolaos Kallimanis, presents a new universal construction for wait-free objects with good theoretical properties  ...  to generate low-stretch spanning subgraphs, and present its applications to improved parallel graph algorithms.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00224-013-9520-x">doi:10.1007/s00224-013-9520-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fpznnggtv5eapmktnk7zus67hm">fatcat:fpznnggtv5eapmktnk7zus67hm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170913112446/https://link.springer.com/content/pdf/10.1007%2Fs00224-013-9520-x.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/27/4d/274d657f20c1ece9663f9bfa74fc13e86e6f0992.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00224-013-9520-x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Optimal implementation of wait-free binary relations [chapter]

Eric Goubault
<span title="">1997</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this article we derive an algorithm for computing the "optimal" wait-free program on two processors that implements a given relation from the semantics of a small atomic read/write shared-memory parallel  ...  This algorithm is compared with the more general algorithm given in [9, 13] based on the participated set algorithm of [1].  ...  In fact, it is well known that this relation cannot be implemented in a wait-free manner on a shared memory machine with atomic read/write registers [4] , whereas the following approximate consensus,  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0030599">doi:10.1007/bfb0030599</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dqolui5oeffothqa7eawz7acau">fatcat:dqolui5oeffothqa7eawz7acau</a> </span>
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Indicators of health system coverage and activity in Ireland during the economic crisis 2008–2014 – From 'more with less' to 'less with less'

Sara Burke, Steve Thomas, Sarah Barry, Conor Keegan
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/u6xsvhwp5fhl7bd62uarvfdsqy" style="color: black;">Health Policy</a> </i> &nbsp;
There were over 57,000 people counted on trolleys in 2013. Graph 3 shows the number of people waiting for inpatient and day-case hospital treatment.  ...  Some progress has been made on each of these, for example accurate figures on outpatient wait times were published for the first time in 2012 [11] .  ... 
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The asynchronous computability theorem for t-resilient tasks

Maurice Herlihy, Nir Shavit
<span title="">1993</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the twenty-fifth annual ACM symposium on Theory of computing - STOC &#39;93</a> </i> &nbsp;
Theorem 5.7 The generalized approximate agree- ment task has no wait-free solution if K has a hole of radius E. 119  ...  When 4 = n, @ sends the vertexes of at least one simplex Tn of bary~(Sn ) to distinct vertexes of P, 5.3 Approximate Agreement approximate agreement task, each Pi starts with an input  ... 
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