Preparing for Disaster: Leveraging Precomputation to Efficiently Repair Graph Structures Upon Failures
Pages 63 - 74
Abstract
Distributed algorithms for constructing structures such as a maximal independent set (MIS) or maximal matching (MM) are well-studied in standard message-passing network models. In this paper, we consider a natural variant of this problem in which we begin with an instance of the graph structure and partition our algorithm execution that follows into two stages. During the first stage after the graph structure is calculated, some additional precomputation is done. In the second stage, an arbitrary collection of k nodes are crashed. The goal is to then repair the structure as efficiently as possible. We are interested in the circumstances under which the repair can be faster than the time required to build the structure from scratch, and focus, in particular, on trade-offs in which extra precomputation rounds during the first stage can be traded for faster repairs during the second.
References
[1]
Alkida Balliu, Sebastian Brandt, Juho Hirvonen, Dennis Olivetti, Mikaël Rabie, and Jukka Suomela. 2019. Lower Bounds for Maximal Matchings and Maximal Independent Sets. In 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019, Baltimore, Maryland, USA, November 9--12, 2019, David Zuckerman (Ed.). IEEE Computer Society, USA, 481--497.
[2]
Leonid Barenboim and Michael Elkin. 2010. Sublogarithmic distributed MIS algorithm for sparse graphs using Nash-Williams decomposition. Distributed Computing 22, 5--6 (2010), 363--379.
[3]
Leonid Barenboim, Michael Elkin, and Fabian Kuhn. 2014. Distributed (" + 1)- Coloring in Linear (in ) Time. SIAM J. Comput. 43, 1 (2014), 72--95.
[4]
Leonid Barenboim, Michael Elkin, Seth Pettie, and Johannes Schneider. 2016. The Locality of Distributed Symmetry Breaking. J. ACM 63, 3 (2016), 45 pages.
[5]
Guy Blelloch, Jeremy Fineman, and Julian Shun. 2012. Greedy Sequential Maximal Independent Set and Matching are Parallel on Average. arXiv:1202.3205 [cs.DS]
[6]
Keren Censor-Hillel, Elad Haramaty, and Zohar Karnin. 2016. Optimal Dynamic Distributed MIS. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing (Chicago, Illinois, USA) (PODC '16). Association for Computing Machinery, New York, NY, USA, 217--226.
[7]
Richard Cole and Uzi Vishkin. 1986. Deterministic coin tossing with applications to optimal parallel list ranking. Information and Control 70, 1 (1986), 32--53.
[8]
Mohsen Ghaffari. 2016. An Improved Distributed Algorithm for Maximal Independent Set. In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms (Arlington, Virginia) (SODA '16). Society for Industrial and Applied Mathematics, USA, 270--277.
[9]
Mohsen Ghaffari, Christoph Grunau. 2020. Improved Deterministic Network Decomposition. arXiv:2007.08253 [cs.DS]
[10]
Nabil Guellati and Hamamache Kheddouci. 2010. A survey on self-stabilizing algorithms for independence, domination, coloring, and matching in graphs. J. Parallel and Distrib. Comput. 70, 4 (2010), 406 -- 415.
[11]
Amos Israeli and Alon Itai. 1986. A fast and simple randomized parallel algorithm for maximal matching. Inform. Process. Lett. 22 (01 1986), 77--80.
[12]
Michael König and Roger Wattenhofer. 2013. On Local Fixing. In Principles of Distributed Systems, Roberto Baldoni, Nicolas Nisse, and Maarten van Steen (Eds.). Springer International Publishing, Cham, 191--205.
[13]
Fabian Kuhn, Thomas Moscibroda, and Rogert Wattenhofer. 2004. What Cannot Be Computed Locally!. In Proceedings of the Twenty-Third Annual ACMSymposium on Principles of Distributed Computing (St. John's, Newfoundland, Canada) (PODC '04). Association for Computing Machinery, New York, NY, USA, 300--309.
[14]
Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. 2016. Local Computation: Lower and Upper Bounds. J. ACM 63, 2, Article 17 (mar 2016), 44 pages.
[15]
Fabian Kuhn and Rotem Oshman. 2011. Dynamic Networks: Models and Algorithms. SIGACT News 42, 1 (March 2011), 82--96.
[16]
Nathan Linial. 1992. Locality in Distributed Graph Algorithms.
[17]
Michael Luby. 1985. A Simple Parallel Algorithm for the Maximal Independent Set Problem. In Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing (Providence, Rhode Island, USA) (STOC '85). Association for Computing Machinery, New York, NY, USA, 1--10.
[18]
Nancy A. Lynch. 1996. Distributed Algorithms. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA.
[19]
Alessandro Panconesi and Aravind Srinivasan. 1996. On the Complexity of Distributed Network Decomposition. Journal of Algorithms 20, 2 (1996), 356--374.
[20]
Johannes Schneider and Roger Wattenhofer. 2010. An optimal maximal independent set algorithm for bounded-independence graphs. Distributed Computing 22, 5--6 (2010), 349--361.
Index Terms
- Preparing for Disaster: Leveraging Precomputation to Efficiently Repair Graph Structures Upon Failures
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Published In
July 2022
464 pages
ISBN:9781450391467
DOI:10.1145/3490148
- General Chair:
- Kunal Agrawal,
- Program Chair:
- I-Ting Angelina Lee
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Published: 11 July 2022
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