It's completely false to say that "we know how schedulers work". The _only_ reason there is confusion in this thread and the 4chan thread is because so few people actually know anything about schedulers. If they did, no one would be confused. The fact that there is confusion at all is basically a huge point for explicitly stating your assumptions.
Moreover, that is essentially the whole point of the field of algorithms. Your job as an algorist is to abstract the algorithm away from the implementation details of wholly separate systems, and make all of your assumptions explicit. If you don't specify it, you can't analyze it. And, if an algorithm has to assume an entire, specific OS and scheduler is implemented under it, then you have gone about your job as an algorist completely wrong.
That is the appeal to practicality. But as if to prove my point, you _do_ end up making assumptions. You are assuming that the scheduler is backed by a priority queue, which is certainly not universally true. You don't get to a hard mathematical bound by waving away a detail as important as the data structure that backs the core sort mechanic. If your approach is to say "y'know, like a _normal_ scheduler", then you should stop and rethink your approach to the problem.
Moreover, that is essentially the whole point of the field of algorithms. Your job as an algorist is to abstract the algorithm away from the implementation details of wholly separate systems, and make all of your assumptions explicit. If you don't specify it, you can't analyze it. And, if an algorithm has to assume an entire, specific OS and scheduler is implemented under it, then you have gone about your job as an algorist completely wrong.
That is the appeal to practicality. But as if to prove my point, you _do_ end up making assumptions. You are assuming that the scheduler is backed by a priority queue, which is certainly not universally true. You don't get to a hard mathematical bound by waving away a detail as important as the data structure that backs the core sort mechanic. If your approach is to say "y'know, like a _normal_ scheduler", then you should stop and rethink your approach to the problem.