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I.e. is it the O(1) scheduler, the CFS scheduler, or an older one?
You can call
I'm not sure how you could distinguish the O(1) scheduler from other obsolete schedulers. You could use the kernel version I suppose, but since distributions applied patches to their shipped kernels, this will be unreliable.
The scheduler of a process can be defined by the programmer, using this funcion man sched_setscheduler
to see the scheduler uses by a process you can use the top command
for change the scheduler of a procces chrt