Lattice Completion Algorithms for Distributed Computations

  • Vijay K. Garg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7702)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AV01]
    Alagar, S., Venkatesan, S.: Techniques to tackle state explosion in global predicate detection. IEEE Transactions on Software Engineering 27(8), 704–714 (2001)CrossRefGoogle Scholar
  2. [CG98]
    Chase, C.M., Garg, V.K.: Detection of global predicates: Techniques and their limitations. Distributed Computing 11(4), 191–201 (1998)CrossRefGoogle Scholar
  3. [CM91]
    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. [DP90]
    Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)zbMATHGoogle Scholar
  5. [Fid89]
    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. [Gan84]
    Ganter, B.: Two basic algorithms in concept analysis. Technical Report 831, Techniche Hochschule, Darmstadt (1984)Google Scholar
  7. [Gar03]
    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. [Gar13]
    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. [GK98]
    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)CrossRefGoogle Scholar
  10. [GM01]
    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. [GW94]
    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)CrossRefGoogle Scholar
  12. [GW97]
    Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations, 1st edn. Springer-Verlag New York, Inc., Secaucus (1997)Google Scholar
  13. [HM84]
    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. [JRJ94]
    Jourdan, G.-V., Rampon, J.-X., Jard, C.: Computing on-line the lattice of maximal antichains of posets. Order 11, 197–210 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  15. [Lam78]
    Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. of the ACM 21(7), 558–565 (1978)zbMATHCrossRefGoogle Scholar
  16. [Mat89]
    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. [MG01]
    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. [NR99]
    Nourine, L., Raynaud, O.: A fast algorithm for building lattices. Inf. Process. Lett. 71(5-6), 199–204 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  19. [NR02]
    Nourine, L., Raynaud, O.: A fast incremental algorithm for building lattices. J. Exp. Theor. Artif. Intell. 14(2-3), 217–227 (2002)zbMATHCrossRefGoogle Scholar
  20. [SY85]
    Strom, R.E., Yemeni, S.: Optimistic recovery in distributed systems. ACM Trans. Comput. Syst. 3(3), 204–226 (1985)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vijay K. Garg
    • 1
  1. 1.Parallel and Distributed Systems Lab, Department of Electrical and Computer EngineeringThe University of Texas at AustinAustinUSA

Personalised recommendations