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Leader election is, together with consensus, one of the most central problemsin distributed computing. This paper presents a distributed algorithm, called\STT, for electing deterministically a leader in an arbitrary network, assumingprocessors have unique identifiers of size $O(\log n)$, where $n$ is the numberof processors. It elects a leader in $O(D +\log n)$ rounds, where $D$ is thediameter of the network, with messages of size $O(1)$. Thus it has a bit roundcomplexity of $O(D +\log n)$. This substantially improves upon the best knownalgorithm whose bit round complexity is $O(D\log n)$. In fact, using the lowerbound by Kutten et al. (2015) and a result of Dinitz and Solomon (2007), weshow that the bit round complexity of \STT is optimal (up to a constantfactor), which is a significant step forward in understanding the interplaybetween time and message optimality for the election problem. Our algorithmrequires no knowledge on the graph such as $n$ or $D$, and the pipeliningtechnique we introduce to break the $O(D\log n)$ barrier is general.

Deterministic Leader Election Takes $\Theta(D + \log n)$ Bit Rounds