Leader Election in Well-Connected Graphs

In this paper, we look at the problem of randomized leader election in synchronous distributed networks with a special focus on message complexity. We provide an algorithm that solves implicit version (where non-leader nodes need not be aware identity leader) any general network $$O(\sqrt{n} \log ^{7/2} n \cdot t_{mix})$$ messages and $$O(t_{mix}\log ^2 n)$$ time, where is number $$t_{mix}$$ refers to mixing time random walk graph G. For several classes well-connected (that have large conductance or alternatively small times e.g., expanders, hypercubes, etc), above result implies extremely efficient (sublinear running messages) algorithms. Correspondingly, show substantial improvement possible over our algorithm, by presenting almost matching lower bound for election. $$\varOmega (\sqrt{n}/\phi ^{3/4})$$ are needed succeeds probability least $$1-o(1)$$ , $$\phi $$ graph. To best knowledge, first work shows dependence between complexity solve connectivity G, which often characterized graph’s . Apart from (m)$$ Kutten et al. (J ACM 62(1):7:1–7:27, 2015) m denotes edges graph), also provides one non-trivial bounds networks.