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Space Bounds for Reliable Storage: Fundamental Limits of Coding

Published: 25 July 2016 Publication History

Abstract

We study the inherent space requirements of reliable storage algorithms in asynchronous distributed systems. A number of recent works have used codes in order to achieve a better storage cost than the well-known replication approach. However, a closer look reveals that they incur extra costs in certain scenarios. Specifically, if multiple clients access the storage concurrently, then existing asynchronous code-based algorithms may store a number of copies of the data that grows linearly with the number of concurrent clients. We prove here that this is inherent. Given three parameters, (1) the data size -- D bits, (2) the concurrency level -- c, and (3) the number of storage node failures that need to be tolerated -- f, we show a lower bound of Omega(min(f,c)D) bits on the space complexity of asynchronous distributed storage algorithms. Intuitively, this implies that the asymptotic storage cost is either as high as with replication, namely O(fD), or as high under concurrency as with the aforementioned code-based algorithms, i.e., O(cD).
We further present a technique for combining erasure codes with replication so as to obtain the best of both. We present an adaptive f-tolerant storage algorithm whose storage cost is O(min(f,c)D). Together, our results show that the space complexity of providing reliable storage in asynchronous distributed systems is Theta(min(f,c)D).

References

[1]
Ittai Abraham, Gregory Chockler, Idit Keidar, and Dahlia Malkhi. Byzantine disk paxos: optimal resilience with byzantine shared memory. Distributed Computing, 18(5), 2006.
[2]
Yehuda Afek, Michael Merritt, and Gadi Taubenfeld. Benign failure models for shared memory. In Distributed Algorithms. Springer, 1993.
[3]
Marcos Kawazoe Aguilera, Ramaprabhu Janakiraman, and Lihao Xu. Using erasure codes efficiently for storage in a distributed system. In Dependable Systems and Networks, 2005. DSN 2005. Proceedings. International Conference on. IEEE, 2005.
[4]
Hagit Attiya, Amotz Bar-Noy, and Danny Dolev. Sharing memory robustly in message-passing systems. Journal of the ACM (JACM), 42(1), 1995.
[5]
Christian Cachin and Stefano Tessaro. Optimal resilience for erasure-coded byzantine distributed storage. In Dependable Systems and Networks, 2006. DSN 2006. International Conference on. IEEE, 2006.
[6]
Viveck Cadambe, Zhiying Wang, and Nancy Lynch. Information-theoretic lower bounds on the storage cost of shared memory emulation. In PODC, 2016.
[7]
Viveck R Cadambe, Nancy Lynch, Muriel Medard, and Peter Musial. A coded shared atomic memory algorithm for message passing architectures. In Network Computing and Applications (NCA), 2014 IEEE 13th International Symposium on. IEEE, 2014.
[8]
Gregory Chockler, Dan Dobre, Alexander Shraer, and Alexander Spiegelman. Space bounds for reliable multi-writer data store: Inherent cost of read/write primitives. arXiv preprint arXiv:1508.03762, 2015.
[9]
Gregory Chockler, Rachid Guerraoui, and Idit Keidar. Amnesic distributed storage. In Distributed Computing. Springer, 2007.
[10]
Partha Dutta, Rachid Guerraoui, and Ron R. Levy. Optimistic erasure-coded distributed storage. In Proceedings of the 22Nd International Symposium on Distributed Computing, DISC '08, Berlin, Heidelberg, 2008. Springer-Verlag.
[11]
Garth R Goodson, Jay J Wylie, Gregory R Ganger, and Michael K Reiter. Efficient byzantine-tolerant erasure-coded storage. In Dependable Systems and Networks, 2004 International Conference on. IEEE, 2004.
[12]
James Hendricks, Gregory R Ganger, and Michael K Reiter. Low-overhead byzantine fault-tolerant storage. In ACM SIGOPS Operating Systems Review, volume 41. ACM, 2007.
[13]
Prasad Jayanti, Tushar Deepak Chandra, and Sam Toueg. Fault-tolerant wait-free shared objects. Journal of the ACM (JACM), 45(3), 1998.
[14]
Leslie Lamport. On interprocess communication. Distributed computing, 1(2), 1986.
[15]
Heverson Borba Ribeiro and Emmanuelle Anceaume. Datacube: A p2p persistent data storage architecture based on hybrid redundancy schema. In Parallel, Distributed and Network-Based Processing (PDP), 2010 18th Euromicro International Conference on. IEEE, 2010.
[16]
Cheng Shao, Jennifer L Welch, Evelyn Pierce, and Hyunyoung Lee. Multiwriter consistency conditions for shared memory registers. SIAM Journal on Computing, 40(1), 2011.
[17]
Alexander Spiegelman, Yuval Cassuto, Gregory Chockler, and Idit Keidar. Space bounds for reliable storage: Fundamental limits of coding. arXiv preprint arXiv:1507.05169, 2015.
[18]
Zhiying Wang and Viveck Cadambe. Multi-version coding in distributed storage. In Information Theory (ISIT), 2014 IEEE International Symposium on. IEEE, 2014.

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  • (2024)Ares II: Tracing the Flaws of a (Storage) God2024 43rd International Symposium on Reliable Distributed Systems (SRDS)10.1109/SRDS64841.2024.00027(187-197)Online publication date: 30-Sep-2024
  • (2022)Self-Stabilizing and Private Distributed Shared Atomic Memory in Seldomly Fair Message Passing NetworksAlgorithmica10.1007/s00453-022-01023-w85:1(216-276)Online publication date: 20-Aug-2022
  • (2021)Consistent Distributed StorageSynthesis Lectures on Distributed Computing Theory10.2200/S01069ED1V01Y202012DCT01720:1(1-192)Online publication date: 28-Jun-2021
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    cover image ACM Conferences
    PODC '16: Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing
    July 2016
    508 pages
    ISBN:9781450339643
    DOI:10.1145/2933057
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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    Published: 25 July 2016

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    Author Tags

    1. algorithm
    2. coding
    3. lower bound
    4. space complexity
    5. storage emulation

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    PODC '16 Paper Acceptance Rate 40 of 149 submissions, 27%;
    Overall Acceptance Rate 740 of 2,477 submissions, 30%

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    View all
    • (2024)Ares II: Tracing the Flaws of a (Storage) God2024 43rd International Symposium on Reliable Distributed Systems (SRDS)10.1109/SRDS64841.2024.00027(187-197)Online publication date: 30-Sep-2024
    • (2022)Self-Stabilizing and Private Distributed Shared Atomic Memory in Seldomly Fair Message Passing NetworksAlgorithmica10.1007/s00453-022-01023-w85:1(216-276)Online publication date: 20-Aug-2022
    • (2021)Consistent Distributed StorageSynthesis Lectures on Distributed Computing Theory10.2200/S01069ED1V01Y202012DCT01720:1(1-192)Online publication date: 28-Jun-2021
    • (2020)Fundamental Limits of Erasure-Coded Key-Value Stores With Side InformationIEEE Transactions on Communications10.1109/TCOMM.2020.298143168:7(4126-4140)Online publication date: Jul-2020
    • (2018)Treeplication: An Erasure Code that is Almost as Painless as Replication2018 IEEE Information Theory Workshop (ITW)10.1109/ITW.2018.8613396(1-5)Online publication date: Nov-2018
    • (2017)A Layered Architecture for Erasure-Coded Consistent Distributed StorageProceedings of the ACM Symposium on Principles of Distributed Computing10.1145/3087801.3087832(63-72)Online publication date: 25-Jul-2017
    • (2017)Space Complexity of Fault-Tolerant Register EmulationsProceedings of the ACM Symposium on Principles of Distributed Computing10.1145/3087801.3087824(83-92)Online publication date: 25-Jul-2017
    • (2016)Information-Theoretic Lower Bounds on the Storage Cost of Shared Memory EmulationProceedings of the 2016 ACM Symposium on Principles of Distributed Computing10.1145/2933057.2933118(305-313)Online publication date: 25-Jul-2016

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