Abstract
When n processes communicate by writing to and reading from k < n MWMR registers the “communication bandwidth” precludes emulation of SWMR system, even non-blocking.
Nevertheless, recently a positive result was shown that such a system either wait-free or obstruction-free can solve an interesting one-shot task. This paper demonstrates another such result. It shows that (n − 1)-set agreement can be solved obstruction-free with merely 2 MWMR registers. Achieving k-set agreement with n − k + 1 registers is a challenge. We make the first step toward it by showing k-set agreement with 2(n − k) registers.
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References
Afek, Y., Attiya, H., Dolev, D., Gafni, E., Merritt, M., Shavit, N.: Atomic snapshots of shared memory. Journal of the ACM 40(4), 873–890 (1993)
Aspnes, J., Ellen, F.: Tight bounds for anonymous adopt-commit objects. In: Rajaraman, R., auf der Heide, F.M. (eds.) Proceedings of the 23rd Annual ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2011(Co-located with FCRC 2011), San Jose, CA, USA, June 4-6, pp. 317–324. ACM (2011)
Attiya, H., Bar-Noy, A., Dolev, D., Peleg, D., Reischuk, R.: Renaming in an asynchronous environment. Journal of the ACM 37(3), 524–548 (1990)
Attiya, H., Fouren, A.: Adaptive and efficient algorithms for lattice agreement and renaming. SIAM J. Comput. 31(2), 642–664 (2002)
Attiya, H., Guerraoui, R., Hendler, D., Kuznetsov, P.: The complexity of obstruction-free implementations. J. ACM 56(4) (2009)
Attiya, H., Welch, J.: Distributed Computing. Fundamentals, Simulations, and Advanced Topics. John Wiley & Sons (2004)
Borowsky, E., Gafni, E.: Generalized FLP impossibility result for t-resilient asynchronous computations. In: STOC, pp. 91–100. ACM Press (1993)
Borowsky, E., Gafni, E.: Immediate atomic snapshots and fast renaming. In: PODC, pp. 41–51. ACM Press (1993)
Borowsky, E., Gafni, E.: A simple algorithmically reasoned characterization of wait-free computation (extended abstract). In: Proceedings of the Sixteenth Annual ACM Symposium on Principles of Distributed Computing, PODC 1997, pp. 189–198. ACM Press, New York (1997)
Burns, J.E., Lynch, N.A.: Bounds on shared memory for mutual exclusion. Inf. Comput. 107(2), 171–184 (1993)
Chaudhuri, S.: More choices allow more faults: Set consensus problems in totally asynchronous systems. Information and Computation 105(1), 132–158 (1993)
Delporte-Gallet, C., Fauconnier, H.: Two Consensus Algorithms with Atomic Registers and Failure Detector Ω. In: Garg, V., Wattenhofer, R., Kothapalli, K. (eds.) ICDCN 2009. LNCS, vol. 5408, pp. 251–262. Springer, Heidelberg (2008)
Delporte-Gallet, C., Fauconnier, H., Gafni, E., Rajsbaum, S.: Linear space bootstrap communication schemes. In: Frey, D., Raynal, M., Sarkar, S., Shyamasundar, R.K., Sinha, P. (eds.) ICDCN 2013. LNCS, vol. 7730, pp. 363–377. Springer, Heidelberg (2013)
Delporte-Gallet, C., Fauconnier, H., Gafni, E., Rajsbaum, S.: Linear space bootstrap communication scheme. Technical report (2013)
Ellen, F., Fatourou, P., Ruppert, E.: The space complexity of unbounded timestamps. Distributed Computing 21(2), 103–115 (2008)
Fich, F.E., Herlihy, M., Shavit, N.: On the space complexity of randomized synchronization. J. ACM 45(5), 843–862 (1998)
Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. Journal of the ACM 32(2), 374–382 (1985)
Gafni, E.: Round-by-round fault detectors (extended abstract): Unifying synchrony and asynchrony. In: Proceedings of the 17th Symposium on Principles of Distributed Computing (1998)
Gafni, E., Mostéfaoui, A., Raynal, M., Travers, C.: From adaptive renaming to set agreement. Theor. Comput. Sci. 410(14), 1328–1335 (2009)
Helmi, M., Higham, L., Pacheco, E., Woelfel, P.: The space complexity of long-lived and one-shot timestamp implementations. In: Proceedings of the 30th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2011, pp. 139–148. ACM, New York (2011)
Herlihy, M.: Wait-free synchronization. ACM Transactions on Programming Languages and Systems 13(1), 123–149 (1991)
Herlihy, M., Luchangco, V., Moir, M.: Obstruction-free synchronization: Double-ended queues as an example. In: 23rd International Conference on Distributed Computing Systems, ICDCS 2003, Providence, RI, USA, May 19-22, pp. 522–529. IEEE Computer Society (2003)
Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. Journal of the ACM 46(2), 858–923 (1999)
Herlihy, M., Shavit, N.: The Art of Multiprocessor Programming. Morgan Kaufmann (2008)
Saks, M., Zaharoglou, F.: Wait-free k-set agreement is impossible: The topology of public knowledge. In: Proceedings of the 25th ACM Symposium on Theory of Computing, pp. 101–110. ACM Press (May 1993)
Saks, M., Zaharoglou, F.: Wait-free k-set agreement is impossible: The topology of public knowledge. SIAM J. on Computing 29, 1449–1483 (2000)
Styer, E., Peterson, G.L.: Tight bounds for shared memory symmetric mutual exclusion problems. In: Proceedings of the Eighth Annual ACM Symposium on Principles of Distributed Computing, PODC 1989, pp. 177–191. ACM, New York (1989)
Yang, J., Neiger, G., Gafni, E.: Structured derivations of consensus algorithms for failure detectors. In: Proceedings of the 17th ACM Symposium on Principles of Distributed Computing, pp. 297–306 (1998)
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Delporte-Gallet, C., Fauconnier, H., Gafni, E., Rajsbaum, S. (2013). Black Art: Obstruction-Free k-set Agreement with |MWMR registers| < |proccesses|. In: Gramoli, V., Guerraoui, R. (eds) Networked Systems. NETYS 2013. Lecture Notes in Computer Science, vol 7853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40148-0_3
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DOI: https://doi.org/10.1007/978-3-642-40148-0_3
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