NDLI: Balls-into-leaves: sub-logarithmic renaming in synchronous message-passing systems

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Balls-into-leaves: sub-logarithmic renaming in synchronous message-passing systems

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Balls-into-leaves: sub-logarithmic renaming in synchronous message-passing systems

Content Provider	ACM Digital Library
Author	Denysyuk, Oksana Shavit, Nir Rodrigues, Luís Alistarh, Dan
Abstract	We consider the following natural problem: n failure-prone servers, communicating synchronously through message passing, must assign themselves one-to-one to n distinct items. Existing literature suggests two possible approaches to this problem. First, model it as an instance of tight renaming in synchronous message-passing systems; for deterministic solutions, a tight bound of Θ(log n) communication rounds is known. Second, model the scenario as an instance of randomized load-balancing, for which elegant sub-logarithmic solutions exist. However, careful examination reveals that known load-balancing schemes do not apply to our scenario, because they either do not tolerate faults or do not ensure one-to-one allocation. It is thus natural to ask if sub-logarithmic solutions exist for this apparently simple but intriguing problem. In this paper, we combine the two approaches to provide a new randomized solution for tight renaming, which terminates in O(log log n) communication rounds with high probability, against a strong adaptive adversary. Our solution, called Balls-into-Leaves, combines the deterministic approach with a new randomized scheme to obtain perfectly balanced allocations. The algorithm arranges the items as leaves of a tree, and participants repeatedly perform random choices among the leaves. The algorithm exchanges information in each round to split the participants into progressively smaller groups whose random choices do not conflict. We then extend the algorithm to terminate early in O(log log f) rounds w.h.p., where f is the actual number of failures. These results imply an exponential separation between deterministic and randomized algorithms for the tight renaming problem in message-passing systems.
Starting Page	232
Ending Page	241
Page Count	10
File Format	PDF
ISBN	9781450329446
DOI	10.1145/2611462.2611499
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-07-15
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Synchronous message-passing model Randomized algorithms Renaming problem
Content Type	Text
Resource Type	Article

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