The Space Complexity of Unbounded Timestamps

The timestamp problem captures a fundamental aspect of asynchronous distributed computing. It allows processes to label events throughout the system with timestamps that provide information about the real-time ordering of those events. We consider the space complexity of wait-free implementations of timestamps from shared read-write registers in a system of n processes. We prove an Ω( √ n) lower bound on the number of registers required. If the timestamps are elements of a nowhere dense set, for example the integers, we prove a stronger, and tight, lower bound of n. However, if timestamps are not from a nowhere dense set, this bound can be beaten; we give an algorithm that uses n − 1 (single-writer) registers. We also consider the special case of anonymous algorithms, where processes do not have unique identifiers. We prove anonymous timestamp algorithms require n registers. We give an algorithm to prove that this lower bound is tight. This is the first anonymous algorithm that...

• Type: Conference
• Year: 2007
• Where: WDAG
• Authors: Faith Ellen, Panagiota Fatourou, Eric Ruppert
• Keywords: Algorithm, Algorithms, Lower Bound, Timestamp, WDAG 2007