Detecting global termination conditions in the face of uncertainty
PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
Leader Election Problem on Networks in which Processor Identity Numbers Are Not Distinct
IEEE Transactions on Parallel and Distributed Systems
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The problem of leader election in an asynchronous network with possible faulty edges (and nodes) is studied. In our model, a faulty edge is an edge which does not transfer messages in both directions. The election is needed in such cases in order to reorganize the network after failures have occurred. The goal is a fault tolerant algorithm with detection of termination. The common methods for the heavily studied termination detection cannot be applied in unreliable networks. Actually, when there is no additional knowledge, it is obvious that no fault tolerant algorithm can guarantee termination detection. However in real networks it is reasonable to expect that some global information, such as ``how many nodes form a majority'''', is known. For this model we present an $0(n ^ 2 + m)$ messages complexity algorithm, and each message is $0(log(MazId))$ bits (where $n$ is number of nodes, $m$ the number of edges and $MaxId$ is the maximum identify.) Before presenting the formal algorithm and proofs, we present an informal description in which we construct our algorithm step by step. The algorithm guarantees termination in a component with a majority of the nodes. This algorithm can be used in networks in which message transmission is not restricted to the FIFO discipline. Thus, the memory (or the time and messages) needed to simulate the FIFO discipline, is saved. The memory space needed in each node is only $0(MaxNodesDegree~+~log(MaxId))$(which, within a constant, is the best possible).