@saji89 mentioned the
uptime command. I'll go one step lower, and simply posit that the sysadmin has a script somewhere that connects to each computer and does a
cat /proc/uptime (or something equivalent). The first field of the output is the time, in seconds, since the system was last rebooted, which is much easier to parse than the output of
uptime. For example, my computer gives a first uptime field of
up 16 days, 16:20. 1441218 seconds is 16 days plus 58818 seconds, and 58818 seconds is 16 1/3 hours. 16 days 16 1/3 hours.
When you know the maximum length of time since the system should have been rebooted, this data makes it trivial to check to see if the system has been rebooted since then or not.
It could be done through a monitoring tool such as Nagios, or through a separate script that the sysadmin keeps on his computer (or rather accessible through it, I'd imagine) which connects to each computer in turn or in parallell and prints the time since last reboot in some format. That all depends on how elaborate to make it.