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The contender nodes are called active and the rest are called passive. Let the number of nodes in the ring be and let the number of active nodes in the beginning be In each round, an active node generates a random number and sends its vote to a node which is hops away. Clearly, is the number of active nodes between the sender and the receiver, including the receiver. The intermediate passive nodes simply relay votes. The nodes that receive a non-empty set of votes in the current round, survive to become contenders in the next round.

With this notion of fairness, we develop fair randomized algorithms for asynchronous ring networks. Our algorithms have an implicit round structure where nodes are elected to progress to the next round by randomized voting. Leader election is achieved by the tight interleaving of solitude detection and attrition procedures. The motivation for such a notion of fairness is natural and useful in real applications in distributed computing. Managing multiple resources in dynamic environments requires election of resource managing nodes.

9. Alon Itai and Michael Rodeh. Symmetry breaking in distributed networks. Information and Computation, 88(1):60–87, 1990. 10. Burns. A formal model for message passing systems. Technical Report TR-91, Indiana University, 1980. 11. G Le Lann. Distributed systems-towards a formal approach. In Proceedings of the IFIP Congress 77, pages 155–160. North-Holland, 1977. unidirectional distributed algorithm for the circu12. Gary L. Peterson. An lar extrema problem. ACM Transactions on Programming Languages and Systems, 4(4):758–762, 1982.

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Digital Image Watermarking using Mixing Systems by Voyatzis Pitas

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