article published yes Dan-Adrian Alistarh author 4A899BFC-F248-11E8-B48F-1D18A9856A870000-0003-3650-940X Faith Ellen author Joel Rybicki author 334EFD2E-F248-11E8-B48F-1D18A9856A870000-0002-6432-6646 DaAl department Elastic Coordination for Scalable Machine Learning project Coordination in constrained and natural distributed systems project 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 node of the graph as input and, if non-faulty, must output a node such that – all the outputs are within distance 1 of one another, and – each output value lies on a shortest path between two input values. From prior work, it is known that there is no wait-free algorithm among processes for this problem on any cycle of length , by reduction from 2-set agreement (Castañeda et al., 2018). In this work, we investigate the solvability of this task on general graphs. We give a new, direct proof of the impossibility of approximate agreement on cycles of length , 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 different class of graphs, which properly contains the class of chordal graphs. https://research-explorer.ista.ac.at/download/12566/12570/2023_TheoreticalCompScience_Alistarh.pdf application/pdfno Elsevier2023 eng 0304-3975 00093426270000110.1016/j.tcs.2023.113733 9482 Alistarh, Dan-Adrian, et al. “Wait-Free Approximate Agreement on Graphs.” <i>Theoretical Computer Science</i>, vol. 948, no. 2, 113733, Elsevier, 2023, doi:<a href="https://doi.org/10.1016/j.tcs.2023.113733">10.1016/j.tcs.2023.113733</a>. Alistarh D-A, Ellen F, Rybicki J. 2023. Wait-free approximate agreement on graphs. Theoretical Computer Science. 948(2), 113733. Alistarh D-A, Ellen F, Rybicki J. Wait-free approximate agreement on graphs. <i>Theoretical Computer Science</i>. 2023;948(2). doi:<a href="https://doi.org/10.1016/j.tcs.2023.113733">10.1016/j.tcs.2023.113733</a> Alistarh, Dan-Adrian, Faith Ellen, and Joel Rybicki. “Wait-Free Approximate Agreement on Graphs.” <i>Theoretical Computer Science</i>. Elsevier, 2023. <a href="https://doi.org/10.1016/j.tcs.2023.113733">https://doi.org/10.1016/j.tcs.2023.113733</a>. D.-A. Alistarh, F. Ellen, J. Rybicki, Theoretical Computer Science 948 (2023). Alistarh, D.-A., Ellen, F., &#38; Rybicki, J. (2023). Wait-free approximate agreement on graphs. <i>Theoretical Computer Science</i>. Elsevier. <a href="https://doi.org/10.1016/j.tcs.2023.113733">https://doi.org/10.1016/j.tcs.2023.113733</a> D.-A. Alistarh, F. Ellen, and J. Rybicki, “Wait-free approximate agreement on graphs,” <i>Theoretical Computer Science</i>, vol. 948, no. 2. Elsevier, 2023. 125662023-02-19T23:00:55Z2025-04-14T07:49:16Z