The Complexity of Renaming

Dan Alistarh, Seth Gilbert, Rachid Guerraoui
Ieee Computer Soc Press, Customer Service Center, Po Box 3014, 10662 Los Vaqueros Circle, Los Alamitos, Ca 90720-1264 Usa, 2011
Article de conférence

We study the complexity of renaming, a fundamental problem in distributed computing in which a set of processes need to pick distinct names from a given namespace. We prove an individual lower bound of Omega(k) process steps for deterministic renaming into any namespace of size sub-exponential in k, where k is the number of participants. This bound is tight: it draws an exponential separation between deterministic and randomized solutions, and implies new tight bounds for deterministic fetch-and-increment registers, queues and stacks. The proof of the bound is interesting in its own right, for it relies on the first reduction from renaming to another fundamental problem in distributed computing: mutual exclusion. We complement our individual bound with a global lower bound of Omega(k log(k/c)) on the total step complexity of renaming into a namespace of size c k, for any c >= 1. This applies to randomized algorithms against a strong adversary, and helps derive new global lower bounds for randomized approximate counter and fetch-and-increment implementations, all tight within logarithmic factors.

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Dan Alistarh, Seth Gilbert, Rachid Guerraoui
Ieee Computer Soc Press, Customer Service Center, Po Box 3014, 10662 Los Vaqueros Circle, Los Alamitos, Ca 90720-1264 Usa, 2011
Article de conférence

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https://infoscience.epfl.ch/record/168239?ln=fr

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Tight Bounds for Asynchronous Renaming

Dan Alistarh, Seth Gilbert, Rachid Guerraoui

This article presents the first tight bounds on the time complexity of shared-memory renaming, a fundamental problem in distributed computing in which a set of processes need to pick distinct identifiers from a small namespace. We first prove an individual lower bound of P(h) process steps for deterministic renaming into any namespace of size subexponential in k, where k is the number of participants. The bound is tight: it draws an exponential separation between deterministic and randomized solutions, and implies new tight bounds for deterministic concurrent fetch-and-increment counters, queues, and stacks. The proof is based on a new reduction from renaming to another fundamental problem in distributed computing: mutual exclusion. We complement this individual bound with a global lower bound of Omega(k log(k/c)) on the total step complexity of renaming into a namespace of size ck, for any c >= 1. This result applies to randomized algorithms against a strong adversary, and helps derive new global lower bounds for randomized approximate counter implementations, that are tight within logarithmic factors. On the algorithmic side, we give a protocol that transforms any sorting network into a randomized strong adaptive renaming algorithm, with expected cost equal to the depth of the sorting network. This gives a tight adaptive renaming algorithm with expected step complexity O(log k), where k is the contention in the current execution. This algorithm is the first to achieve sublinear time, and it is time-optimal as per our randomized lower bound. Finally, we use this renaming protocol to build monotone-consistent counters with logarithmic step complexity and linearizable fetch-and-increment registers with polylogarithmic cost.

Association for Computing Machinery2014

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Asynchronous task allocation is a fundamental problem in distributed computing, in which p asyn- chronous processes must execute a set of m tasks. Also known as write-all or do-all, this problem been studied extensively, both independently and as a key building block for various distributed algorithms. In this paper, we break new ground on this classic problem: we introduce the To-DoTree concurrent data structure, which improves on the best known random- ized and deterministic upper bounds. In the presence of an adaptive adversary, the randomized To-DoTree algorithm has O(m+plogplog2m) work complexity. We then show that there exists a deterministic vari- ant of the To-DoTree algorithm with work complexity O(m+p log5 m log2 max(m, p)). For all values of m and p, our algorithms are within log factors of the Ω(m + p log p) lower bound for this problem. The key technical ingredient in our results is a new approach for analyzing concurrent executions against a strong adaptive scheduler. This technique allows us to handle the complex dependencies between the processes’ coin flips and their scheduling, and to tightly bound the work needed to perform subsets of the tasks. We believe this technique will be useful in the analysis of other, more complex, concurrent data structures.

2012

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How to Allocate Tasks Asynchronously

Dan Alistarh, Seth Gilbert, Rachid Guerraoui

Asynchronous task allocation is a fundamental problem in distributed computing in which p asynchronous processes must execute a set of m tasks. Also known as write-all or do-all, this problem been studied extensively, both independently and as a key building block for various distributed algorithms. In this paper, we break new ground on this classic problem: we introduce the To-Do Tree concurrent data structure, which improves on the best known randomized and deterministic upper bounds. In the presence of an adaptive adversary, the randomized To-Do Tree algorithm has O(m+p log p log2 m) work complexity. We then show that there exists a deterministic variant of the To-Do Tree algorithm with work complexity O(m+p log5 m log2 max(m, p)). For all values of m and p, our algorithms are within log factors of the O(m + p log p) lower bound for this problem. The key technical ingredient in our results is a new approach for analyzing concurrent executions against a strong adaptive scheduler. This technique allows us to handle the complex dependencies between the processes' coin flips and their scheduling, and to tightly bound the work needed to perform subsets of the tasks.

IEEE2012

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