  We study a public event scheduling problem, where multiple public events are
scheduled to coordinate the availability of multiple agents. The availability
of each agent is determined by solving a separate flexible interval job
scheduling problem, where the jobs are required to be preemptively processed.
The agents want to attend as many events as possible, and their agreements are
considered to be the total length of time during which they can attend these
events. The goal is to find a schedule for events as well as the job schedule
for each agent such that the total agreement is maximized.
  We first show that the problem is NP-hard, and then prove that a simple
greedy algorithm achieves $\frac{1}{2}$-approximation when the whole timeline
is polynomially bounded. Our method also implies a
$(1-\frac{1}{e})$-approximate algorithm for this case. Subsequently, for the
general timeline case, we present an algorithmic framework that extends a
$\frac{1}{\alpha}$-approximate algorithm for the one-event instance to the
general case that achieves $\frac{1}{\alpha+1}$-approximation. Finally, we give
a polynomial time algorithm that solves the one-event instance, and this
implies a $\frac{1}{2}$-approximate algorithm for the general case.
