{"year":"2021","intvolume":"     12810","volume":12810,"language":[{"iso":"eng"}],"_id":"9823","citation":{"mla":"Alistarh, Dan-Adrian, et al. “Wait-Free Approximate Agreement on Graphs.” <i>Structural Information and Communication Complexity</i>, vol. 12810, Springer Nature, 2021, pp. 87–105, doi:<a href=\"https://doi.org/10.1007/978-3-030-79527-6_6\">10.1007/978-3-030-79527-6_6</a>.","ieee":"D.-A. Alistarh, F. Ellen, and J. Rybicki, “Wait-free approximate agreement on graphs,” in <i>Structural Information and Communication Complexity</i>, Wrocław, Poland, 2021, vol. 12810, pp. 87–105.","ama":"Alistarh D-A, Ellen F, Rybicki J. Wait-free approximate agreement on graphs. In: <i>Structural Information and Communication Complexity</i>. Vol 12810. Springer Nature; 2021:87-105. doi:<a href=\"https://doi.org/10.1007/978-3-030-79527-6_6\">10.1007/978-3-030-79527-6_6</a>","apa":"Alistarh, D.-A., Ellen, F., &#38; Rybicki, J. (2021). Wait-free approximate agreement on graphs. In <i>Structural Information and Communication Complexity</i> (Vol. 12810, pp. 87–105). Wrocław, Poland: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-79527-6_6\">https://doi.org/10.1007/978-3-030-79527-6_6</a>","ista":"Alistarh D-A, Ellen F, Rybicki J. 2021. Wait-free approximate agreement on graphs. Structural Information and Communication Complexity. SIROCCO: Structural Information and Communication Complexity, LNCS, vol. 12810, 87–105.","chicago":"Alistarh, Dan-Adrian, Faith Ellen, and Joel Rybicki. “Wait-Free Approximate Agreement on Graphs.” In <i>Structural Information and Communication Complexity</i>, 12810:87–105. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/978-3-030-79527-6_6\">https://doi.org/10.1007/978-3-030-79527-6_6</a>.","short":"D.-A. Alistarh, F. Ellen, J. Rybicki, in:, Structural Information and Communication Complexity, Springer Nature, 2021, pp. 87–105."},"conference":{"end_date":"2021-07-01","location":"Wrocław, Poland","name":"SIROCCO: Structural Information and Communication Complexity","start_date":"2021-06-28"},"external_id":{"arxiv":["2103.08949"]},"publication_identifier":{"issn":["03029743"],"eissn":["16113349"],"isbn":["9783030795269"]},"doi":"10.1007/978-3-030-79527-6_6","page":"87-105","author":[{"last_name":"Alistarh","first_name":"Dan-Adrian","full_name":"Alistarh, Dan-Adrian","id":"4A899BFC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3650-940X"},{"last_name":"Ellen","first_name":"Faith","full_name":"Ellen, Faith"},{"orcid":"0000-0002-6432-6646","last_name":"Rybicki","first_name":"Joel","id":"334EFD2E-F248-11E8-B48F-1D18A9856A87","full_name":"Rybicki, Joel"}],"publication":"Structural Information and Communication Complexity","alternative_title":["LNCS"],"quality_controlled":"1","title":"Wait-free approximate agreement on graphs","status":"public","publisher":"Springer Nature","scopus_import":"1","oa":1,"oa_version":"Preprint","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","date_created":"2021-08-08T22:01:29Z","department":[{"_id":"DaAl"}],"main_file_link":[{"url":"https://arxiv.org/abs/2103.08949","open_access":"1"}],"abstract":[{"lang":"eng","text":"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. In this work, we consider a natural generalisation of approximate agreement on arbitrary undirected connected graphs. Each process is given a vertex of the graph as input and, if non-faulty, must output a vertex such that\r\nall the outputs are within distance 1 of one another, and\r\n\r\neach output value lies on a shortest path between two input values.\r\n\r\nFrom prior work, it is known that there is no wait-free algorithm among   𝑛≥3  processes for this problem on any cycle of length   𝑐≥4 , by reduction from 2-set agreement (Castañeda et al. 2018).\r\n\r\nIn this work, we investigate the solvability and complexity of this task on general graphs. We give a new, direct proof of the impossibility of approximate agreement on cycles of length   𝑐≥4 , via a generalisation of Sperner’s Lemma to convex polygons. We also extend the reduction from 2-set agreement to a larger class of graphs, showing that approximate agreement on these graphs is unsolvable. On the positive side, we present a wait-free algorithm for a class of graphs that properly contains the class of chordal graphs."}],"date_published":"2021-06-20T00:00:00Z","publication_status":"published","month":"06","article_processing_charge":"No","date_updated":"2023-02-23T14:09:49Z","type":"conference","day":"20"}