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Maximal Antichain Lattice Algorithms for Distributed Computations

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Distributed Computing and Networking (ICDCN 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7730))

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Abstract

The lattice of maximal antichains of a distributed computation is generally much smaller than its lattice of consistent global states. We show that a useful class of predicates can be detected on the lattice of maximal antichains instead of the lattice of consistent cuts obtaining significant (exponential for many cases) savings. We then propose new online and offline algorithms to construct and enumerate the lattice of maximal antichains. Previously known algorithm by Nourine and Raynoud [NR99, NR02] to construct the lattice takes O(n 2 m) time where n is the number of events in the computation, and m is the size of the lattice of maximal antichains. The algorithm by Jourdan, Rampon and Jard [JRJ94] takes O((n + w 2)wm) time where w is the width of the computation. All these algorithms assume as input the lattice of maximal antichains prior to the arrival of a new event. We present a new online incremental algorithm, OLMA, that computes the newly added elements to the lattice without requiring the prior lattice. Since the lattice may be exponential in the size of the computation, we get a significant reduction in the space complexity. The OLMA algorithm takes O(mw 2 logw L ) time and O(w L w logn) space where w L is the width of the lattice of maximal antichains. The lower space complexity makes our algorithm applicable for online global predicate detection in a distributed system. For the purposes of analyzing offline traces, we also propose new enumeration algorithms to traverse the lattice.

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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. Chandy, K.M., Lamport, L.: Distributed snapshots: Determining global states of distributed systems. ACM Trans. Comput. Syst. 3(1), 63–75 (1985)

    Article  Google Scholar 

  4. 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 

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

    MATH  Google Scholar 

  6. 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 (1989)

    Google Scholar 

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

    Google Scholar 

  8. Garg, V.K.: Lattice completion algorithms for distributed computations. In: Proc. of Principles of Distributed Systems - 16th International Conference, OPODIS 2012 (December 2012)

    Google Scholar 

  9. Garg, V.K., Mittal, N.: On slicing a distributed computation. In: 21st Intnatl. Conf. on Distributed Computing Systems (ICDCS 20 01), Washington, Brussels, Tokyo, pp. 322–329. IEEE (2001)

    Google Scholar 

  10. Ikiz, S., Garg, V.K.: Efficient incremental optimal chain partition of distributed program traces. In: ICDCS, p. 18. IEEE Computer Society (2006)

    Google Scholar 

  11. 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 

  12. 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 

  13. Mattern, F.: Virtual time and global states of distributed systems. In: Parallel and Distributed Algorithms: Proc. of the Intnatl. Workshop on Parallel and Distributed Algorithms, pp. 215–226. Elsevier Science Publishers B.V., North-Holland (1989)

    Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. 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 

  17. Reuter, K.: The jump number and the lattice of maximal antichains. Discrete Mathematics 88(23), 289–307 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  18. Tomlinson, A.I., Garg, V.K.: Detecting relational global predicates in distributed systems. In: Proc. of the Workshop on Parallel and Distributed Debugging, San Diego, CA, pp. 21–31 (May 1993)

    Google Scholar 

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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

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  1. Vijay K. Garg
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Editors and Affiliations

  1. IRISA/INRIA-Rennes, Campus Universitaire de Beaulieu, Campus Universitaire de Beaulieu, 35042, Rennes Cedex, France

    Davide Frey

  2. IRISA-ISTIC Université de Rennes 1, Institut Universitaire de France, Campus Universitaire de Beaulieu, 35042, Rennes Cedex, France

    Michel Raynal

  3. Department of Electrical and Systems Engineering, University of Pennsylvania, 200 S. 33rd Street, 19104, Philadelphia, PA, USA

    Saswati Sarkar

  4. Faculty of Technology and Computer Science, Tata Institute of Fundamental Research, Homi Bhabha Road, 400005, Mumbai, India

    Rudrapatna K. Shyamasundar

  5. Department of Computer Science and Engineering, 791 Drees Labs, The Ohio State University, 2015 Neil Avenue, 43210-1277, Columbus, OH, USA

    Prasun Sinha

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Garg, V.K. (2013). Maximal Antichain Lattice Algorithms for Distributed Computations. In: Frey, D., Raynal, M., Sarkar, S., Shyamasundar, R.K., Sinha, P. (eds) Distributed Computing and Networking. ICDCN 2013. Lecture Notes in Computer Science, vol 7730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35668-1_17

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  • DOI: https://doi.org/10.1007/978-3-642-35668-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35667-4

  • Online ISBN: 978-3-642-35668-1

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