Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-28T01:12:44.709Z Has data issue: false hasContentIssue false
  • English
  • Français

Back to the Coordinated Attack Problem

Published online by Cambridge University Press:  09 July 2021

Emmanuel Godard Open the ORCID record for Emmanuel Godard [Opens in a new window]  and
Eloi Perdereau
Emmanuel Godard*
Affiliation:
Laboratoire d’Informatique et Systèmes, Aix-Marseille Université – CNRS (UMR 7020), Marseille, France
Eloi Perdereau
Affiliation:
Laboratoire d’Informatique et Systèmes, Aix-Marseille Université – CNRS (UMR 7020), Marseille, France
*
*Corresponding author Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the well-known Coordinated Attack Problem, where two generals have to decide on a common attack, when their messengers can be captured by the enemy. Informally, this problem represents the difficulties to agree in the presence of communication faults. We consider here only omission faults (loss of message), but contrary to previous studies, we do not to restrict the way messages can be lost, i.e., we make no specific assumption, we use no specific failure metric. In the large subclass of message adversaries where the double simultaneous omission can never happen, we characterize which ones are obstructions for the Coordinated Attack Problem. We give two proofs of this result. One is combinatorial and uses the classical bivalency technique for the necessary condition. The second is topological and uses simplicial complexes to prove the necessary condition. We also present two different Consensus algorithms that are combinatorial (resp. topological) in essence. Finally, we analyze the two proofs and illustrate the relationship between the combinatorial approach and the topological approach in the very general case of message adversaries. We show that the topological characterization gives a clearer explanation of why some message adversaries are obstructions or not. This result is a convincing illustration of the power of topological tools for distributed computability.

Keywords

Distributed systemsfault-tolerancemessage-passingsynchronous systemscoordinated attack problemtwo generals problemtwo armies problemconsensusmessage adversariesomission faultsdistributed computabilitysimplicial complexestopological methods
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 10 , November 2020 , pp. 1089 - 1113
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adagio, G. (2003). Using the topological characterization of synchronous models. Electronic Notes in Theoretical Computer Science 81 36–47.CrossRefGoogle Scholar
Afek, Y. and Gafni, E. (2013). Asynchrony from Synchrony, Lecture Notes in Computer Science, vol. 7730, Berlin Heidelberg, Springer, 225–239.Google Scholar
Aguilera, M. K. and Toueg, S. (1999). A simple bivalency proof that -resilient consensus requires + 1 rounds. Information Processing Letters 71 (3–4) 155–158.CrossRefGoogle Scholar
Akkoyunlu, E. A., Ekanadham, K. and Huber, R. V. (1975). Some constraints and tradeoffs in the design of network communications. In: Proceedings of the fifth ACM Symposium on Operating Systems Principles, Austin, TX, USA, ACM, 67–74.CrossRefGoogle Scholar
Borowsky, E. and Gafni, E. (1993). Generalized flp impossibility result for t-resilient asynchronous computations. In: STOC’93: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, New York, NY, USA, ACM Press, 91–100.CrossRefGoogle Scholar
Charron-Bost, B., Guerraoui, R. and Schiper, A. (2000). Synchronous system and perfect failure detector: Solvability and efficiency issue. In: DSN, IEEE Computer Society, 523–532.CrossRefGoogle Scholar
Charron-Bost, B. and Schiper, A. (2009) The heard-of model: Computing in distributed systems with benign faults. Distributed Computing 22 (1) 49–71.CrossRefGoogle Scholar
Coulouma, É., Godard, E. and Peters, J. G. (2015). A characterization of oblivious message adversaries for which consensus is solvable. Theoretical Computer Science 584 80–90.CrossRefGoogle Scholar
Chaudhuri, S., Herlihy, M., Lynch, N. A. and Tuttle, M. R. (2000). Tight bounds for k-set agreement. Journal of the ACM 47 (5) 912–943.CrossRefGoogle Scholar
Fevat, T. and Godard, E. (2011) Minimal obstructions for the coordinated attack problem and beyond. In: 2011 IEEE International on Parallel Distributed Processing Symposium (IPDPS), May 2011, 1001–1011.CrossRefGoogle Scholar
Fischer, M. J., Lynch, N. A. and Paterson, M. S. (1985) Impossibility of distributed consensus with one faulty process. Journal of the ACM 32 (2) 374–382.CrossRefGoogle Scholar
Gafni, E., Kuznetsov, P. and Manolescu, C. (2014) A generalized asynchronous computability theorem. In: Halldórsson, M. M. and Dolev, S. (eds.) ACM Symposium on Principles of Distributed Computing, PODC’14, Paris, France, July 15–18, 2014, ACM, 222–231.CrossRefGoogle Scholar
Guerraoui, R., Kouznetsov, P. and Pochon, B. (2003) A note on set agreement with omission failures. Electronic Notes in Theoretical Computer Science 81 48–58.CrossRefGoogle Scholar
Gray, J. (1978). Notes on data base operating systems. In: Operating Systems, An Advanced Course, London, UK, Springer-Verlag, 393–481.CrossRefGoogle Scholar
Herlihy, M., Kozlov, D. N. and Rajsbaum, S. (2013). Distributed Computing Through Combinatorial Topology, Morgan Kaufmann. ISBN 978-0-12-404578-1.Google Scholar
Herlihy, M. and Shavit, N. (1999). The topological structure of asynchronous computability. Journal of the ACM 46(6), 858–923.CrossRefGoogle Scholar
Kuznetsov, P. Personal Communication.Google Scholar
Lynch, N. A. (1996). Distributed Algorithms, San Francisco, CA, USA, Morgan Kaufmann Publishers Inc.Google Scholar
Moses, Y. and Rajsbaum, S. (1998). The unified structure of consensus: A layered analysis approach. In: PODC, 123–132.CrossRefGoogle Scholar
Munkres, J. R. (1984) Elements of Algebraic Topology, Addison Wesley Publishing Company. ISBN 978-0-201627282.Google Scholar
Nowak, T., Schmid, U. and Winkler, K. (2019). Topological characterization of consensus under general message adversaries. In: PODC, ACM, 218–227.CrossRefGoogle Scholar
Pease, L., Shostak, R. and Lamport, L. (1980). Reaching agreement in the presence of faults. Journal of the ACM 27(2), 228–234.CrossRefGoogle Scholar
Perdereau, E. (2015). Caractérisation topologique du problème des deux généraux. Master’s thesis, Université Aix-Marseille.Google Scholar
Pin, J. E. and Perrin, D. (2004). Infinite Words, Pure and Applied Mathematics, vol. 141, Elsevier. ISBN 978-0-12-532111-2.Google Scholar
Raynal, M. (2002). Consensus in synchronous systems:a concise guided tour. In: Pacific Rim International Symposium on Dependable Computing, IEEE, 0:221.Google Scholar
Saks, M. and Zaharoglou, F. (2000). wait-free k-set agreement is impossible: The topology of public knowledge. SIAM Journal on Computing 29 1449–1483.CrossRefGoogle Scholar
Santoro, N. (2006). Design and Analysis of Distributed Algorithms, Wiley. ISBN 978-0-471-71997-7.CrossRefGoogle Scholar
Santoro, N. and Widmayer, P. (1989). Time is not a healer. In STACS 89, Lecture Notes in Computer Science, vol. 349. Berlin Heidelberg, Springer, 304–313.CrossRefGoogle Scholar
Santoro, N. and Widmayer, P. (2007). Agreement in synchronous networks with ubiquitous faults. Theoretical Computer Science 384 (2–3) 232–249.CrossRefGoogle Scholar