On achieving consensus using a shared memory
PODC '88 Proceedings of the seventh annual ACM Symposium on Principles of distributed computing
Logical Time in Distributed Computing Systems
Computer - Distributed computing systems: separate resources acting as one
Concerning the size of logical clocks in distributed systems
Information Processing Letters
Bounds on shared memory for mutual exclusion
Information and Computation
A bounded first-in, first-enabled solution to the l-exclusion problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
How to share concurrent wait-free variables
Journal of the ACM (JACM)
Bounded Concurrent Time-Stamping
SIAM Journal on Computing
On the space complexity of randomized synchronization
Journal of the ACM (JACM)
Simple and efficient bounded concurrent timestamping and the traceable use abstraction
Journal of the ACM (JACM)
SIAM Journal on Computing
Time, clocks, and the ordering of events in a distributed system
Communications of the ACM
A new solution of Dijkstra's concurrent programming problem
Communications of the ACM
Bounded concurrent timestamp systems using vector clocks
Journal of the ACM (JACM)
Time and Space Lower Bounds for Nonblocking Implementations
SIAM Journal on Computing
A Concurrent Time-Stamp Scheme which is Linear in Time and Space
WDAG '92 Proceedings of the 6th International Workshop on Distributed Algorithms
Algorithms adapting to point contention
Journal of the ACM (JACM)
Distributed Computing
Time-space tradeoffs for implementations of snapshots
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Atomic shared register access by asynchronous hardware
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Computing on a partially eponymous ring
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
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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 uses a finite number of registers. Although this algorithm is wait-free, its step complexity is not bounded. We also present an algorithm that uses Ω(n2) registers and has bounded step complexity.