Tight bounds for k-set agreement
Journal of the ACM (JACM)
Lower Bounds in Distributed Computing
DISC '00 Proceedings of the 14th International Conference on Distributed Computing
A New Synchronous Lower Bound for Set Agreement
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Wait-Free n-Set Consensus When Inputs Are Restricted
DISC '02 Proceedings of the 16th International Conference on Distributed Computing
Hundreds of impossibility results for distributed computing
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
An adaptive collect algorithm with applications
Distributed Computing
The combined power of conditions and failure detectors to solve asynchronous set agreement
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Irreducibility and additivity of set agreement-oriented failure detector classes
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Tight bounds for k-set agreement with limited-scope failure detectors
Distributed Computing - Special issue: DISC 03
Anti-Ω: the weakest failure detector for set agreement
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
New combinatorial topology upper and lower bounds for renaming
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
The Iterated Restricted Immediate Snapshot Model
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Local Maps: New Insights into Mobile Agent Algorithms
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
A topological treatment of early-deciding set-agreement
Theoretical Computer Science
From adaptive renaming to set agreement
Theoretical Computer Science
An Axiomatic Approach to Computing the Connectivity of Synchronous and Asynchronous Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
The disagreement power of an adversary: extended abstract
Proceedings of the 28th ACM symposium on Principles of distributed computing
Narrowing power vs efficiency in synchronous set agreement: Relationship, algorithms and lower bound
Theoretical Computer Science
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Visiting Gafni's Reduction Land: From the BG Simulation to the Extended BG Simulation
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
The Minimum Information about Failures for Solving Non-local Tasks in Message-Passing Systems
OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
Weak Synchrony Models and Failure Detectors for Message Passing (k-)Set Agreement
OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
Of Choices, Failures and Asynchrony: The Many Faces of Set Agreement
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
From renaming to set agreement
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Revisiting the impossibility for boosting service resilience
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Narrowing power vs. efficiency in synchronous set agreement
ICDCN'08 Proceedings of the 9th international conference on Distributed computing and networking
Multi-sided shared coins and randomized set-agreement
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
The disagreement power of an adversary
DISC'09 Proceedings of the 23rd international conference on Distributed computing
The price of anonymity: optimal consensus despite asynchrony, crash and anonymity
DISC'09 Proceedings of the 23rd international conference on Distributed computing
The multiplicative power of consensus numbers
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
The topology of shared-memory adversaries
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
The failure detector abstraction
ACM Computing Surveys (CSUR)
Concurrent computing and shellable complexes
DISC'10 Proceedings of the 24th international conference on Distributed computing
Brief announcement: new bounds for partially synchronous set agreement
DISC'10 Proceedings of the 24th international conference on Distributed computing
Recursion in distributed computing
SSS'10 Proceedings of the 12th international conference on Stabilization, safety, and security of distributed systems
On adaptive renaming under eventually limited contention
SSS'10 Proceedings of the 12th international conference on Stabilization, safety, and security of distributed systems
An intuitionistic epistemic logic for sequential consistency on shared memory
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
(anti-Ωx × Σz)-based k-set agreement algorithms
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
Distributed programming with tasks
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
Distributed decision problems: the locality angle
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Transforming worst-case optimal solutions for simultaneous tasks into all-case optimal solutions
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
The Price of Anonymity: Optimal Consensus Despite Asynchrony, Crash, and Anonymity
ACM Transactions on Autonomous and Adaptive Systems (TAAS)
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
A non-topological proof for the impossibility of k-set agreement
SSS'11 Proceedings of the 13th international conference on Stabilization, safety, and security of distributed systems
Relations linking failure detectors associated with k-set agreement in message-passing systems
SSS'11 Proceedings of the 13th international conference on Stabilization, safety, and security of distributed systems
Mathematical models of object-based distributed systems
Formal modeling
DISC'11 Proceedings of the 25th international conference on Distributed computing
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
A topological treatment of early-deciding 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
Simultaneous consensus tasks: a tighter characterization of set-consensus
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
New combinatorial topology bounds for renaming: The upper bound
Journal of the ACM (JACM)
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Subconsensus tasks: renaming is weaker than set agreement
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Early-stopping k-set agreement in synchronous systems prone to any number of process crashes
PaCT'05 Proceedings of the 8th international conference on Parallel Computing Technologies
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Optimal randomized fair exchange with secret shared coins
OPODIS'05 Proceedings of the 9th international conference on Principles of Distributed Systems
The committee decision problem
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Easy impossibility proofs for k-set agreement in message passing systems
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
Renaming is weaker than set agreement but for perfect renaming: a map of sub-consensus tasks
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Electronic Notes in Theoretical Computer Science (ENTCS)
An Introduction to the Topological Theory of Distributed Computing with Safe-consensus
Electronic Notes in Theoretical Computer Science (ENTCS)
The renaming problem in shared memory systems: An introduction
Computer Science Review
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
A closer look at fault tolerance
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Weakening failure detectors for k-set agreement via the partition approach
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Computability in distributed computing: a Tutorial
ACM SIGACT News
Counting-based impossibility proofs for renaming and set agreement
DISC'12 Proceedings of the 26th international conference on Distributed Computing
A non-topological proof for the impossibility of k-set agreement
Theoretical Computer Science
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In the classical consensus problem, each of n processors receives a private input value and produces a decision value which is one of the original input values, with the requirement that all processors decide the same value. A central result in distributed computing is that, in several standard models including the asynchronous shared-memory model, this problem has no deterministic solution. The k-set agreement problem is a generalization of the classical consensus proposed by Chaudhuri [ Inform. and Comput., 105 (1993), pp. 132--158], where the agreement condition is weakened so that the decision values produced may be different, as long as the number of distinct values is at most k. For $nk\geq 2$ it was not known whether this problem is solvable deterministically in the asynchronous shared memory model. In this paper, we resolve this question by showing that for any k n, there is no deterministic wait-free protocol for n processors that solves the k-set agreement problem. The proof technique is new: it is based on the development of a topological structure on the set of possible processor schedules of a protocol. This topological structure has a natural interpretation in terms of the knowledge of the processors of the state of the system. This structure reveals a close analogy between the impossibility of wait-free k-set agreement and the Brouwer fixed point theorem for the k-dimensional ball.