Efficient Reduction for Wait-Free Termination Detection in a Crash-Prone Distributed System
We investigate the problem of detecting termination of a distributed computation in systems where processes can fail by crashing. Specifically, when the communication topology is fully connected, we describe a way to transform any termination detection algorithm $\mathcal{A}$ that has been designed...
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| Published in | Distributed Computing pp. 93 - 107 |
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| Main Authors | , , , |
| Format | Book Chapter |
| Language | English |
| Published |
Berlin, Heidelberg
Springer Berlin Heidelberg
2005
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| Series | Lecture Notes in Computer Science |
| Subjects | |
| Online Access | Get full text |
| ISBN | 3540291636 9783540291633 |
| ISSN | 0302-9743 1611-3349 |
| DOI | 10.1007/11561927_9 |
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| Summary: | We investigate the problem of detecting termination of a distributed computation in systems where processes can fail by crashing. Specifically, when the communication topology is fully connected, we describe a way to transform any termination detection algorithm $\mathcal{A}$ that has been designed for a failure-free environment into a termination detection algorithm $\mathcal{B}$ that can tolerate process crashes. Our transformation assumes the existence of a perfect failure detector. We show that a perfect failure detector is in fact necessary to solve the termination detection problem in a crash-prone distributed system even if at most one process can crash.
Let μ(n,M) and δ(n,M) denote the message complexity and detection latency, respectively, of $\mathcal{A}$ when the system has n processes and the underlying computation exchanges M application messages. The message complexity of $\mathcal{B}$ is at most O(n + μ(n,0)) messages per failure more than the message complexity of $\mathcal{A}$ . Also, its detection latency is at most O(δ(n,0)) per failure more than that of $\mathcal{A}$ . Furthermore, the overhead (that is, the amount of control data piggybacked) on an application message increases by only O(log n) bits per failure.
The fault-tolerant termination detection algorithm resulting from the transformation satisfies two desirable properties. First, it can tolerate failure of up to n–1 processes, that is, it is wait-free. Second, it does not impose any overhead on the fault-sensitive termination detection algorithm until one or more processes crash, that is, it is fault-reactive. Our transformation can be extended to arbitrary communication topologies provided process crashes do not partition the system. |
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| Bibliography: | Original Abstract: We investigate the problem of detecting termination of a distributed computation in systems where processes can fail by crashing. Specifically, when the communication topology is fully connected, we describe a way to transform any termination detection algorithm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A}$\end{document} that has been designed for a failure-free environment into a termination detection algorithm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{B}$\end{document} that can tolerate process crashes. Our transformation assumes the existence of a perfect failure detector. We show that a perfect failure detector is in fact necessary to solve the termination detection problem in a crash-prone distributed system even if at most one process can crash. Let μ(n,M) and δ(n,M) denote the message complexity and detection latency, respectively, of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A}$\end{document} when the system has n processes and the underlying computation exchanges M application messages. The message complexity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{B}$\end{document} is at most O(n + μ(n,0)) messages per failure more than the message complexity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A}$\end{document}. Also, its detection latency is at most O(δ(n,0)) per failure more than that of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A}$\end{document}. Furthermore, the overhead (that is, the amount of control data piggybacked) on an application message increases by only O(log n) bits per failure. The fault-tolerant termination detection algorithm resulting from the transformation satisfies two desirable properties. First, it can tolerate failure of up to n–1 processes, that is, it is wait-free. Second, it does not impose any overhead on the fault-sensitive termination detection algorithm until one or more processes crash, that is, it is fault-reactive. Our transformation can be extended to arbitrary communication topologies provided process crashes do not partition the system. |
| ISBN: | 3540291636 9783540291633 |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/11561927_9 |