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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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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

  • eBook Packages: Computer ScienceComputer Science (R0)

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