# Achieving Efficiency, Robustness, and Security in Distributed Computing

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This dissertation investigates ways to improve various performance metrics of distributed computing systems. We begin with a study of the \emph{message complexity} of the \emph{leader election} problem in diameter-two networks. We first give a simple randomized Monte-Carlo leader election algorithm that with high probability\footnote{Throughout this dissertation, we would use `eith high probability'' or `

whp'' to mean ``with probability at least