### The Space Complexity of Long-Lived and One-Shot Timestamp ImplementationsThe Space Complexity of Long-Lived and One-Shot Timestamp Implementations

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 Author Helmi, Maryam ♦ Higham, Lisa ♦ Pacheco, Eduardo ♦ Woelfel, Philipp Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2014 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Timestamps ♦ Obstruction-free ♦ Shared memory ♦ Solo-termination ♦ Space complexity ♦ Wait-free Abstract This article is concerned with the problem of implementing an unbounded timestamp object from multiwriter atomic registers, in an asynchronous distributed system of $\textit{n}$ processes with distinct identifiers where timestamps are taken from an arbitrary universe. Ellen et al. [2008] showed that $√\textit{n}/2$ ™ $\textit{O}(1)$ registers are required for any obstruction-free implementation of long-lived timestamp systems from atomic registers (meaning processes can repeatedly get timestamps). We improve this existing lower bound in two ways. First we establish a lower bound of $\textit{n}/6$ ™ 1 registers for the obstruction-free long-lived timestamp problem. Previous such linear lower bounds were only known for constrained versions of the timestamp problem. This bound is asymptotically tight; Ellen et al. [2008] constructed a wait-free algorithm that uses $\textit{n}$ ™ 1 registers. Second we show that $√2\textit{n}$ ™ log $\textit{n}$ ™ $\textit{O}(1)$ registers are required for any obstruction-free implementation of one-shot timestamp systems (meaning each process can get a timestamp at most once). We show that this bound is also asymptotically tight by providing a wait-free one-shot timestamp system that uses at most $⌈2√\textit{n}⌉$ registers, thus establishing a space complexity gap between one-shot and long-lived timestamp systems. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2014-01-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 61 Issue Number 1 Page Count 25 Starting Page 1 Ending Page 25

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Source: ACM Digital Library