I am not following, isn't this just a graph that shows that how fast operations happen is largely dependent on the odds that it is in cache at various levels (CPU/Ram/Disk)?

The memory operation itself is O(1), around 100 ns, where at a certain point we are doing full ram fetches each time because the odds of it being in CPU cache are low?

Typically O notation is an upper bound, and it holds well there.

That said, due to cache hits, the lower bound is much lower than that.

You see similar performance degradation if you iterate in a double sided array the in the wrong index first.

Memory access performance depends on the _maximum size of memory you need to address_. You can clearly see it in the graph of that article where L1, L2, L3 and RAM are no longer enough to fit the linked list. However while the working set fits in them the performance scales much better. So as long as you give priority to the working set, you can fill the rest of the biggest memory with whatever you want without affecting performance.

RAM is always storing something, it’s just sometimes zeros or garbage. Nothing in how DRAM timings work is sensitive to what bits are encoded in each cell.

> Every byte used makes the whole thing slower.

This is an incorrect conclusion to make from the link you posted in the context of this discussion. That post is a very long-winded way of saying that the average speed of addressing N elements depends on N and the size of the caches, which isn't news to anyone. Key word: addressing.

Huh? There is nothing called "empty memory". There is always something being stored in the memory, the important thing is whether you care about that specific bits or not.

And no, the articles you linked is about caching, not RAM access. Hardware-wise, it doesn't matter what you have in the cells, access latency is the same. There is gonna be some degradation with #read/write cycles, but that is besides the point.

why is it not O(1)? It has to service within a deadline time, so it is still constant.

The author of that post effectively re-defines "memory"/"RAM" as "data", and uses that to say "accessing data in the limit scales to N x sqrt(N) as N increases". Which, like, yeah? Duh, I can't fit 200PB of data into the physical RAM of my computer and the more data I have to access the slower it'll be to access any part of it without working harder at other abstraction layers to bring the time taken down. That's true. It's also unrelated to what people are talking about when they say "memory access is O(1)". When people say "memory access is O(1)" they are talking about cases where their data fits in memory (RAM).

Their experimental results would in fact be a flat line IF they could disable all the CPU caches, even though performance would be slow.