  This paper provides three nearly-optimal algorithms for scheduling $t$ jobs
in the $\mathsf{CLIQUE}$ model. First, we present a deterministic scheduling
algorithm that runs in $O(\mathsf{GlobalCongestion} + \mathsf{dilation})$
rounds for jobs that are sufficiently efficient in terms of their memory. The
$\mathsf{dilation}$ is the maximum round complexity of any of the given jobs,
and the $\mathsf{GlobalCongestion}$ is the total number of messages in all jobs
divided by the per-round bandwidth of $n^2$ of the $\mathsf{CLIQUE}$ model.
Both are inherent lower bounds for any scheduling algorithm.
  Then, we present a randomized scheduling algorithm which runs $t$ jobs in
$O(\mathsf{GlobalCongestion} + \mathsf{dilation}\cdot\log{n}+t)$ rounds and
only requires that inputs and outputs do not exceed $O(n\log n)$ bits per node,
which is met by, e.g., almost all graph problems. Lastly, we adjust the
\emph{random-delay-based} scheduling algorithm [Ghaffari, PODC'15] from the
$\mathsf{CLIQUE}$ model and obtain an algorithm that schedules any $t$ jobs in
$O(t / n + \mathsf{LocalCongestion} + \mathsf{dilation}\cdot\log{n})$ rounds,
where the $\mathsf{LocalCongestion}$ relates to the congestion at a single node
of the $\mathsf{CLIQUE}$. We compare this algorithm to the previous approaches
and show their benefit.
  We schedule the set of jobs on-the-fly, without a priori knowledge of its
parameters or the communication patterns of the jobs. In light of the inherent
lower bounds, all of our algorithms are nearly-optimal.
  We exemplify the power of our algorithms by analyzing the message complexity
of the state-of-the-art MIS protocol [Ghaffari, Gouleakis, Konrad, Mitrovic and
Rubinfeld, PODC'18], and we show that we can solve $t$ instances of MIS in $O(t
+ \log\log\Delta\log{n})$ rounds, that is, in $O(1)$ amortized time, for $t\geq
\log\log\Delta\log{n}$.
