Linearizability: a correctness condition for concurrent objects
ACM Transactions on Programming Languages and Systems (TOPLAS)
Renaming in an asynchronous environment
Journal of the ACM (JACM)
ACM Transactions on Programming Languages and Systems (TOPLAS)
Atomic snapshots of shared memory
Journal of the ACM (JACM)
Immediate atomic snapshots and fast renaming
PODC '93 Proceedings of the twelfth annual ACM symposium on Principles of distributed computing
Generalized FLP impossibility result for t-resilient asynchronous computations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
More choices allow more faults: set consensus problems in totally asynchronous systems
Information and Computation
Failure detectors and the wait-free hierarchy (extended abstract)
Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing
The weakest failure detector for solving consensus
Journal of the ACM (JACM)
Fast, wait-free (2k-1)-renaming
Proceedings of the eighteenth annual ACM symposium on Principles of distributed computing
The topological structure of asynchronous computability
Journal of the ACM (JACM)
k-set agreement with limited accuracy failure detectors
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge
SIAM Journal on Computing
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Mathematical Structures in Computer Science
Distributed Computing: Fundamentals, Simulations and Advanced Topics
Distributed Computing: Fundamentals, Simulations and Advanced Topics
Tight bounds for k-set agreement with limited-scope failure detectors
Distributed Computing - Special issue: DISC 03
In search of the holy grail: looking for the weakest failure detector for wait-free set agreement
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Renaming with k-set-consensus: an optimal algorithm into n + k - 1 slots
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
The weakest failure detectors to boost obstruction-freedom
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Locks Considered Harmful: A Look at Non-traditional Synchronization
SEUS '08 Proceedings of the 6th IFIP WG 10.2 international workshop on Software Technologies for Embedded and Ubiquitous Systems
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The M-renaming problem consists in providing the processes with a new name taken from a new name space of size M. A renaming algorithm is adaptive if the size M depends on the number of processes that want to acquire a new name (and not on the total number n of processes). Assuming each process proposes a value, the k-set agreement problem allows each process to decide a proposed value in such a way that at most k different values are decided. In an asynchronous system prone to up to t process crash failures, and where processes can cooperate by accessing atomic read/write registers only, the best that can be done is a renaming space of size M = p+t where p is the number of processes that participate in the renaming. In the same setting, the k-set agreement problem cannot be solved for t ≥ k. This paper focuses on the way a solution to the renaming problem can help solving the k-set agreement problem when k ≤ t. It has several contributions. The first is a t-resilient algorithm (1 ≤ t n) that solves the k-set agreement problem from any adaptive (n + k - 1)-renaming algorithm, when k = t. The second contribution is a lower bound that shows that there is no wait-free k-set algorithm based on an (n+k -1)- renaming algorithm that works for any value of n, when k t. This bound shows that, while a solution to the (n + k - 1)-renaming problem allows solving the k-set agreement problem despite t = k failures, such an additional power is useless when k t. In that sense, in an asynchronous system made up of atomic registers, (n + k - 1)-renaming allows progressing from k t to k = t, but does not allow by passing that frontier. The last contribution of the paper is a wait-free algorithm that constructs an adaptive (n + k - 1)-renaming algorithm, for any value of the pair (t, k), from a failure detector of the class Ω*k (this last algorithm is a simple adaptation of an existing renaming algorithm).