Improved Deterministic Leader Election in Diameter-Two Networks
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In this paper, we investigate the leader election problem in diameter-two networks. Recently, Chatterjee et al. [DC 2020] studied the leader election in diameter-two networks. They presented a O(log n)-round deterministic implicit leader election algorithm which incurs optimal O(nlog n) messages, but a drawback of their algorithm is that it requires knowledge of n. An important question – whether it is possible to remove the assumption on the knowledge of n was left open in their paper. Another interesting open question raised in their paper is whether explicit leader election can be solved in Õ(n) messages deterministically. In this paper, we give an affirmative answer to them. Further, we solve the broadcast problem, another fundamental problem in distributed computing, deterministically in diameter-two networks with Õ(n) messages and Õ(1) rounds without the knowledge of n. In fact, we address all the open questions raised by Chatterjee et al. for the deterministic leader election problem in diameter-two networks. To the best of our knowledge, this is the first Õ(n) deterministic result for the explicit leader election in the diameter-two networks, that too without the knowledge of n.
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