STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Parallel symmetry-breaking in sparse graphs
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Computing on an anonymous ring
Journal of the ACM (JACM)
On the number of rounds necessary to disseminate information
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
A trade-off between information and communication in broadcast protocols
Journal of the ACM (JACM)
Fast gossiping for the hypercube
SIAM Journal on Computing
Locality in distributed graph algorithms
SIAM Journal on Computing
Single round simulation on radio networks
Journal of Algorithms
Journal of Computer and System Sciences
Methods and problems of communication in usual networks
Proceedings of the international workshop on Broadcasting and gossiping 1990
Theoretical Computer Science
Fault-local distributed mending (extended abstract)
Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing
On the complexity of distributed network decomposition
Journal of Algorithms
Exploring unknown environments
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Exploring unknown undirected graphs
Journal of Algorithms
Fast broadcasting and gossiping in radio networks
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Local computations on static and dynamic graphs
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Deterministic broadcasting in ad hoc radio networks
Distributed Computing
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We consider two interrelated tasks in a synchronous $n$-node ring: distributed constant colouring and local communication. We investigate the impact of the amount of knowledge available to nodes on the time of completing these tasks. Every node knows the labels of nodes up to a distance $r$ from it, called the knowledge radius. In distributed constant colouring every node has to assign itself one out of a constant number of colours, so that adjacent nodes get different colours. In local communication every node has to communicate a message to both of its neighbours. We study these problems in two popular communication models: the one-way model, in which each node can only either transmit to one neighbour or receive from one neighbour, in any round, and the radio model, in which simultaneous receiving from two neighbours results in interference noise. Hence the main problem in fast execution of the above tasks is breaking symmetry with restricted knowledge of the ring.We show that distributed constant colouring and local communication are tightly related and one can be used to accomplish the other. Also, in most situations the optimal time is the same for both of them, and it strongly depends on knowledge radius. For knowledge radius $r=0$, i.e., when each node knows only its own label, our bounds on time for both tasks are tight in both models: the optimal time in the one-way model is $\Theta(n)$, while in the radio model it is $\Theta(\log n)$. For knowledge radius $r=1$ both tasks can be accomplished in time $O(\log \log n)$ in the one-way model, if the ring is oriented. For $2 \leq r \leq c \log ^* n$, where $c