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An O(1) scheduler (pronounced "O of 1 scheduler", "Big O of 1 scheduler", or "constant time scheduler") is a kernel scheduling design that can schedule processes within a constant amount of time, regardless of how many processes are running on the operating system. This is an improvement over previously used O(n) schedulers, which schedule processes in an amount of time that scales linearly based on the amounts of inputs.
In the realm of real-time operating systems, deterministic execution is key, and an O(1) scheduler is able to provide scheduling services with a fixed upper-bound on execution times.
The O(1) scheduler was used in Linux releases 2.6.0 thru 2.6.22 (2003-2007), at which point it was superseded by the Completely Fair Scheduler.