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International Conference On Principles Of Distributed Systems

OPODIS 2012: Principles of Distributed Systems pp 166–180Cite as

Lattice Completion Algorithms for Distributed Computations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7702))

Abstract

A distributed computation is usually modeled as a finite partially ordered set (poset) of events. Many operations on this poset require computing meets and joins of subsets of events. The lattice of normal cuts of a poset is the smallest lattice that embeds the poset such that all meets and joins are defined. In this paper, we propose new algorithms to construct or enumerate the lattice of normal cuts. Our algorithms are designed for distributed computing applications and have lower time or space complexity than those of existing algorithms. We also show applications of this lattice to the problems in distributed computing such as finding the extremal events and detecting global predicates.

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References

  1. Alagar, S., Venkatesan, S.: Techniques to tackle state explosion in global predicate detection. IEEE Transactions on Software Engineering 27(8), 704–714 (2001)

    Article  Google Scholar 

  2. Chase, C.M., Garg, V.K.: Detection of global predicates: Techniques and their limitations. Distributed Computing 11(4), 191–201 (1998)

    Article  Google Scholar 

  3. Cooper, R., Marzullo, K.: Consistent detection of global predicates. In: Proc. of the Workshop on Parallel and Distributed Debugging, Santa Cruz, CA, pp. 163–173 (May 1991)

    Google Scholar 

  4. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  5. Fidge, C.J.: Partial orders for parallel debugging. In: Proc. of the ACM SIGPLAN/SIGOPS Workshop on Parallel and Distributed Debugging, vol. 24(1), pp. 183–194 (January 1989)

    Google Scholar 

  6. Ganter, B.: Two basic algorithms in concept analysis. Technical Report 831, Techniche Hochschule, Darmstadt (1984)

    Google Scholar 

  7. Garg, V.K.: Enumerating global states of a distributed computation. In: Intl Conf. on Parallel and Distributed Computing and Systems, pp. 134–139 (November 2003)

    Google Scholar 

  8. Garg, V.K.: Maximal antichain lattice algorithms for distributed computations. In: Proc. of Distributed Computing and Networking - 14th International Conference, ICDCN 2013 (January 2013)

    Google Scholar 

  9. Ganter, B., Kuznetsov, S.O.: Stepwise Construction of the Dedekind-MacNeille Completion. In: Mugnier, M.-L., Chein, M. (eds.) ICCS 1998. LNCS (LNAI), vol. 1453, pp. 295–302. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  10. Garg, V.K., Mittal, N.: On slicing a distributed computation. In: 21st Intnatl. Conf. on Distributed Computing Systems, ICDCS 2001, pp. 322–329. IEEE, Washington (2001)

    Google Scholar 

  11. Garg, V.K., Waldecker, B.: Detection of weak unstable predicates in distributed programs. IEEE Trans. on Parallel and Distributed Systems 5(3), 299–307 (1994)

    Article  Google Scholar 

  12. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations, 1st edn. Springer-Verlag New York, Inc., Secaucus (1997)

    Google Scholar 

  13. Halpern, J.Y., Moses, Y.: Knowledge and common knowledge in a distributed environment. In: Kameda, T., Misra, J., Peters, J., Santoro, N. (eds.) PODC, pp. 50–61. ACM (1984)

    Google Scholar 

  14. Jourdan, G.-V., Rampon, J.-X., Jard, C.: Computing on-line the lattice of maximal antichains of posets. Order 11, 197–210 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  15. Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. of the ACM 21(7), 558–565 (1978)

    Article  MATH  Google Scholar 

  16. Mattern, F.: Virtual time and global states of distributed systems. In: Proc. of the Intl. Workshop on Parallel and Distributed Algorithms, pp. 215–226 (1989)

    Google Scholar 

  17. Mittal, N., Garg, V.K.: On detecting global predicates in distributed computations. In: 21st Intnatl. Conf. on Distributed Computing Systems, ICDCS 2001, pp. 3–10. IEEE, Washington (2001)

    Google Scholar 

  18. Nourine, L., Raynaud, O.: A fast algorithm for building lattices. Inf. Process. Lett. 71(5-6), 199–204 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  19. Nourine, L., Raynaud, O.: A fast incremental algorithm for building lattices. J. Exp. Theor. Artif. Intell. 14(2-3), 217–227 (2002)

    Article  MATH  Google Scholar 

  20. Strom, R.E., Yemeni, S.: Optimistic recovery in distributed systems. ACM Trans. Comput. Syst. 3(3), 204–226 (1985)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Parallel and Distributed Systems Lab, Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, 78712, USA

    Vijay K. Garg

Authors
  1. Vijay K. Garg
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Automatica e Gestionale, Università degli Studi di Roma “La Sapienza”, Via Ariosto 25, 00168, Rome, Italy

    Roberto Baldoni

  2. School of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward Street, K1N 6N5, Ottawa, ON, Canada

    Paola Flocchini

  3. Electrical and Computing Engineering Dept., Virginia Technical University, 302 Whittemore Street, 24061, Blacksburg, VA, USA

    Ravindran Binoy

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© 2012 Springer-Verlag Berlin Heidelberg

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Garg, V.K. (2012). Lattice Completion Algorithms for Distributed Computations. In: Baldoni, R., Flocchini, P., Binoy, R. (eds) Principles of Distributed Systems. OPODIS 2012. Lecture Notes in Computer Science, vol 7702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35476-2_12

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  • DOI: https://doi.org/10.1007/978-3-642-35476-2_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35475-5

  • Online ISBN: 978-3-642-35476-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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