2011/03/29 by Helmi, Maryam, Higham, Lisa, Pacheco, Eduardo +1
#D.1.3 #Distributed #F.2.m #FOS: Computer and information sciences #Parallel #and Cluster Computing (cs.DC)
paper · doi:10.48550/arxiv.1103.5794
This paper is concerned with the problem of implementing an unbounded timestamp object from multi-writer atomic registers, in an asynchronous distributed system of n processors with distinct identifiers where timestamps are taken from an arbitrary universe. Ellen, Fatourou and Ruppert (2008) showed that sqrtn/2-O(1) registers are required for any obstruction-free implementation of long-lived timestamp systems from atomic registers (meaning processors can repeatedly get timestamps). We improve this existing lower bound in two ways. First we establish a lower bound of n/6 - O(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, Fatourou and Ruppert (2008) constructed a wait-free algorithm that uses n-1 registers. Second we show that sqrtn - O(1) registers are required for any obstruction-free implementation of one-shot timestamp systems(meaning each processor 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 fewer than 2 sqrtn registers, thus establishing a space complexity gap between one-shot and long-lived timestamp systems.