Abstract
In agreement problems, each process has an input value and must choose a decision (output) value. Given \(n\ge 2\) processes and \(m \ge 2\) possible different input values, we want to design an agreement algorithm that enables as many processes as possible to decide on the (same) input value of one of the processes in the presence of t crash failures. Without communication, when each process simply decides on its input value, at least \(\lceil (n-t)/m \rceil \) of the processes are guaranteed to always decide on the same value. Can we do better with communication? For some cases, for example, when \(m=2\), even in the presence of a single crash failure, the answer is negative in a deterministic asynchronous system where communication is either by using atomic read/write registers or by sending and receiving messages. The answer is positive in other cases.
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Notes
- 1.
There are no synchrony assumptions whatsoever. A process that finishes phase one, immediately starts participating in phase two.
References
Aguilera, M.K., Toueg, S.: A simple bivalency proof that \(t\)-resilient consensus requires \(t+1\) rounds. Inf. Process. Lett. 71(3), 155–158 (1999)
Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations and Advanced Topics, 2nd edn. Wiley, Hoboken (2004)
Bassler, B.: Quorum Sensing: How Bacteria Communicate. The Explorer’s Guide to Biology, 48 p. (2019). https://explorebiology.org/summary/cell-biology/quorum-sensing:-how-bacteria-communicate
Borowsky, E., Gafni, E.: Generalized FLP impossibility result for \(t\)-resilient asynchronous computations. In: Proceedings of the 25th ACM Symposium on Theory of Computing, pp. 91–100 (1993)
Chan, D., Hadzilacos, V., Toueg, S.: Bounded disagreement. Theor. Comput. Sci. 826–827, 12–24 (2020). Special issue on OPODIS 2016
Chaudhuri, S.: More choices allow more faults: set consensus problems in totally asynchronous systems. Inf. Comput. 105(1), 132–158 (1993)
Chaudhuri, S., Herlihy, M., Lynch, N., Tuttle, M.: Tight bounds for k-set agreement. J. ACM 47(5), 912–943 (2000)
Dolev, D., Strong, H.R.: Authenticated algorithms for byzantine agreement. SIAM J. Comput. 12(4), 656–666 (1983)
Dwork, C., Peleg, D., Pippenger, N., Upfal, E.: Fault tolerance in networks of bounded degree. SIAM J. Comput. 17(5), 975–988 (1988)
Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)
Fuqua, W.C., Winans, S.C., Greenberg, E.P.: Quorum sensing in bacteria: the LuxR-LuxI family of cell density-responsive transcriptional regulators. J. Bacteriol. 176(2), 269–275 (1994)
Herlihy, M.P.: Wait-free synchronization. ACM Trans. Program. Lang. Syst. 13(1), 124–149 (1991)
Herlihy, M.P., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)
Loui, M., Abu-Amara, H.: Memory requirements for agreement among unreliable asynchronous processes. Adv. Comput. Res. 4, 163–183 (1987)
Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. J. ACM 27(2), 228–234 (1980)
Pratt, S.C.: Quorum sensing by encounter rates in the ant Temnothorax albipennis. Behav. Ecol. 16(2), 488–496 (2005)
Saks, M., Zaharoglou, F.: Wait-free \(k\)-set agreement is impossible: the topology of public knowledge. SIAM J. Comput. 29, 1449–1483 (2000)
Seeley, T.D., Visscher, P.K.: Group decision making in nest-site selection by honey bees. Apidologie 35(2), 101–16 (2004)
Taubenfeld, G.: A closer look at fault tolerance. Theory Comput. Syst. 62, 1085–1108 (2018). Conf. version appeared in PODC 2012
Taubenfeld, G.: Reaching agreement among \(k\) out of \(n\) processes (2023). https://arxiv.org/abs/2205.04873. arXiv:2205.04873v3
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Taubenfeld, G. (2024). Reaching Agreement Among k out of n Processes. In: Emek, Y. (eds) Structural Information and Communication Complexity. SIROCCO 2024. Lecture Notes in Computer Science, vol 14662. Springer, Cham. https://doi.org/10.1007/978-3-031-60603-8_24
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