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Motivated by crowdsourced computation, peer-grading, and recommendationsystems, Braverman, Mao and Weinberg [STOC'16] studied the \emph{query} and\emph{round} complexity of fundamental problems such as finding the maximum(\textsc{max}), finding all elements above a certain value(\textsc{threshold-$v$}) or computing the top$-k$ elements (\textsc{Top}-$k$)in a noisy environment.  For example, consider the task of selecting papers for a conference. Thistask is challenging due the crowdsourcing nature of peer reviews: the resultsof reviews are noisy and it is necessary to parallelize the review process asmuch as possible. We study the noisy value model and the noisy comparisonmodel: In the \emph{noisy value model}, a reviewer is asked to evaluate asingle element: "What is the value of paper $i$?" (\eg accept). In the\emph{noisy comparison model} (introduced in the seminal work of Feige, Peleg,Raghavan and Upfal [SICOMP'94]) a reviewer is asked to do a pairwisecomparison: "Is paper $i$ better than paper $j$?"  In this paper, we show optimal worst-case query complexity for the\textsc{max},\textsc{threshold-$v$} and \textsc{Top}-$k$ problems. For\textsc{max} and \textsc{Top}-$k$, we obtain optimal worst-case upper and lowerbounds on the round vs query complexity in both models. For\textsc{threshold}-$v$, we obtain optimal query complexity and nearly-optimalround complexity, where $k$ is the size of the output) for both models.  We then go beyond the worst-case and address the question of the importanceof knowledge of the instance by providing, for a large range of parameters,instance-optimal algorithms with respect to the query complexity. Furthermore,we show that the value model is strictly easier than the comparison model.

Instance-Optimality in the Noisy Value-and Comparison-Model --- Accept, Accept, Strong Accept: Which Papers get in?