This reminds me of sleep sort. For those unfamiliar, sleepsort is where you have an unsorted array, then have 1 thread per element sleep for the amount of time specified by that element, then append it to a list.
Though sleep sort is obnoxious (& hilarious), I'm sure it could be of use in educational situations. It's both elegant and intuitive. Thought provoking, maybe?
It's kind of like claiming you have an O(n) sorting algorithm because you can run an O(n) selection algorithm to find the kth smallest element for each of 0..n-1 and then run n of them in parallel on n cores to get an O(n) sorting algorithm. If you actually have n cores then the wall clock time for executing that algorithm will be O(n), but the number of operations won't be and it all falls apart when you run out of hardware parallelism.
It reminds of me of bucket sort. There is an intellectually curious implementation to sort a list of unique fixed-width (e.g. 32-bit) integers that goes like this: You allocate an m bit (e.g. 2^32 bit / 512MByte) array and zero it (O(m)), then you inspect every element and set that bit of the array (O(n)), then you traverse the array and add an element to the end of the sorted list for every set bit (O(m)). So the overall algorithm is actually O(1) in the number of elements, because you're doing m+n+m work where m > n, which means you're doing at most m+m+m. The problem is that in practice for most real lists the constant factor is so much larger than n that using an O(n log n) sorting algorithm will be significantly faster. And it's clearly Do Not Use if you're sorting e.g. 128-bit ints. But for n sufficiently close to m it can actually be useful. It would probably be tough to beat for sorting a 3 billion element array of 32-bit ints. Or a 200 element array of 8-bit ints.
Not necessarily (though yes, in any efficient real life it would). It could wait for a tick of the clock and on each scan an unordered list of things to see if any are due to happen.
Of course if the list gets big enough that the list takes a long time to scan then it will break sleep sort because if enough time passes for two or more events to have happened between two checks, those events will happen in an undefined order.
It is a good example of how algorithm design can be done naively and algorithm analysis can be done badly, so definitely has at least some educational value.
Excluding implementation specific edge cases that would break the underlying assumptions regarding thread wakeup times, it is a O(N) time complexity sort in all (best, worst, average) cases. A miracle! Get thee to the patent office! Eat my shorts Shell!
Of course the constant time multiplier involved is so massive that it would not do better than an n(log n) or even an n*n sort in any practical situation, and this is before considering space requirements and thread processing overhead.
The OS needs to pick which thread to run from a pool of N threads - absolute best case an O(log N) operation, either when the thread is queued or when it's being selected. This happens N times, so the runtime seems like it would actually scale as O(N log N).
On the other hand, if you've got a scheduler that can pick the thread with the smallest sleep time from a list in O(1) time, you could just use whatever algorithm that's using to make an O(N) insertion sort...
So while that overhead could increase processing time, wall-clock time need to be affected.
Again this is why I think it makes a good example for illustrating critical thinking in the area of algorithm design and analysis. It is an obviously silly example which could actually work, within certain practical boundaries, and the many obvious problems with it are hidden in more complex processes/structures.