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

This article is concerned with the problem of implementing an unbounded timestamp object from multiwriter atomic registers, in an asynchronous distributed system of n processes with distinct identifiers where timestamps are taken from an arbitrary universe. Ellen et al. [2008] showed that √n/2 − 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 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 n − 1 registers. Second we show that √2n − log n − 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√n⌉ registers, thus establishing a space complexity gap between one-shot and long-lived timestamp systems.