Agreement is harder than consensus: set consensus problems in totally asynchronous systems
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
ACM Transactions on Programming Languages and Systems (TOPLAS)
Generalized FLP impossibility result for t-resilient asynchronous computations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Wait-free k-set agreement is impossible: the topology of public knowledge
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
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
The decidability of distributed decision tasks (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Towards a topological characterization of asynchronous complexity
PODC '97 Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing
The topological structure of asynchronous computability
Journal of the ACM (JACM)
Tight bounds for k-set agreement
Journal of the ACM (JACM)
Distributed Algorithms
A classification of wait-free loop agreement tasks
Theoretical Computer Science - Special issue: Distributed computing
The Impossibility of Boosting Distributed Service Resilience
ICDCS '05 Proceedings of the 25th IEEE International Conference on Distributed Computing Systems
Asynchronous deterministic rendezvous in graphs
Theoretical Computer Science
Tight bounds for asynchronous randomized consensus
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
How to meet in anonymous network
Theoretical Computer Science
Achievable cases in an asynchronous environment
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Mobile agent rendezvous: a survey
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Computability in distributed computing: a Tutorial
ACM SIGACT News
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The rendezvous is a type of distributed decision tasks including many well-known tasks such as set agreement, simplex agreement, and approximation agreement. An n-dimensional rendezvous task, n=1, allows n+2 distinct input values, and each execution produces at most n+2 distinct output values. A rendezvous task is said to implement another if an instance of its solution, followed by a protocol based on shared read/write registers, solves the other. The notion of implementation induces a classification of rendezvous tasks of every dimension: two tasks belong to the same class if they implement each other. Previous work on classifying rendezvous tasks only focused on 1-dimensional ones. This paper solves an open problem by presenting the classification of nice rendezvous of arbitrary dimension. An n-dimensional rendezvous task is said to be nice if the qth reduced homology group of its decision space is trivial for qn, and free for q=n. Well-known examples are set agreement, simplex agreement, and approximation agreement. Each n-dimensional rendezvous task is assigned an algebraic signature, which consists of the nth homology group of the decision space, as well as a distinguished element in the group. It is shown that an n-dimensional nice rendezvous task implements another if and only if there is a homomorphism from its signature to that of the other. Hence the computational power of a nice rendezvous task is completely characterized by its signature. In each dimension, there are infinitely many classes of rendezvous tasks, and exactly countable classes of nice ones. A representative is explicitly constructed for each class of nice rendezvous tasks.