Computing on an anonymous ring
Journal of the ACM (JACM)
Computing on an anonymous network
PODC '88 Proceedings of the seventh annual ACM Symposium on Principles of distributed computing
Better computing on the anonymous ring
Journal of Algorithms
Computing Boolean functions on anonymous networks
Information and Computation
Theoretical Computer Science
Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases
IEEE Transactions on Parallel and Distributed Systems
Comparison of initial conditions for distributed algorithms on anonymous networks
Proceedings of the eighteenth annual ACM symposium on Principles of distributed computing
Computing anonymously with arbitrary knowledge
Proceedings of the eighteenth annual ACM symposium on Principles of distributed computing
Reaching Agreement in the Presence of Faults
Journal of the ACM (JACM)
Distributed Algorithms
The Wakeup Problem in Synchronous Broadcast Systems
SIAM Journal on Discrete Mathematics
Local and global properties in networks of processors (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Broadcasting Algorithms in Radio Networks with Unknown Topology
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Deterministic broadcasting in ad hoc radio networks
Distributed Computing
The wake-up problem in multi-hop radio networks
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A better wake-up in radio networks
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Consensus and mutual exclusion in a multiple access channel
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Distributed agreement with optimal communication complexity
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Scalable quantum consensus for crash failures
DISC'10 Proceedings of the 24th international conference on Distributed computing
On the wake-up problem in radio networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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We consider the message complexity of achieving consensus in synchronous anonymous message passing systems. Unlabeled processors (nodes) communicate through links of a network. In each round every processor can exchange messages with all neighbors and the duration of each transmission is one round. An adversary wakes up some subset of processors at possibly different times and assigns them arbitrary numerical input values. All other processors are dormant and do not have input values. Any message wakes up a dormant processor. The goal of consensus is to wake up all processors and have them agree on one of the input values. We seek deterministic consensus algorithms using as few messages as possible. As opposed to most of the literature on consensus, the difficulty of our scenario are not faults (we assume that the network is fault-free) but the arbitrary network topology combined with the anonymity of nodes. For unknown n-node networks we show a consensus algorithm using O(n2) messages; this complexity is optimal for this class. We show that if the network is known, then the complexity of consensus decreases significantly. Our main contribution is an algorithm that uses O(n3/2log2n) messages on any n-node network and we show that some networks require Ω(nlogn) messages to achieve consensus. We also observe that availability of distinct labels of nodes helps to improve complexity of consensus for known networks but has no effect for the class of unknown networks. Indeed, even with labeled nodes, Ω(n2) messages are sometimes necessary if the network is unknown but for known labeled networks consensus can be always achieved with O(n) messages.