Is there any RMQ algoritm with single element update and less time complexity than segment tree?
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no
No.
If there is, we can sort in faster than
time.
Keep getting the smallest element, and update it to ∞ after.
But, it's already a well-known fact that there's no way to sort in faster than
time (unless data has some special properties like counting sort or radix sort).
So, it's not possible.