A modular technique for the design of efficient distributed leader finding algorithms

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Abstract
A general, modular technique for designing efficient leader finding algorithms in distributed, asynchronous networks is developed. This technique reduces the problem of efficient leader finding to a simpler problem of efficient serial traversing of the corresponding network. The message complexity of the resulting leader finding algorithms is bounded by [f(n) +n)(log2k+ 1) (or (f(m) +n)(log2k+ 1)], wherenis the number of nodes in the network [mis the number of edges in the network],kis the number of nodes that start the algorithm, andf(n) [f(m)] is the message complexity of traversing the nodes [edges] of the network. The time complexity of these algorithms may be as large as their message complexity. This technique does not require that the FIFO discipline is obeyed by the links. The local memory needed for each node, besides the memory needed for the traversal algorithm, is logarithmic in the maximal identity of a node in the network. This result achieves in a unified way the best known upper bounds on the message complexity of leader finding algorithms for circular, complete, and general networks. It is also shown to be applicable to other classes of networks, and in some cases the message complexity of the resulting algorithms is better by a constant factor than that of previously known algorithms.

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