[1] https://www3.cs.stonybrook.edu/~bender/newpub/BenderFaFi07.p...
Both structures exploit the fact that most of the data does not change much and can be packed as tight as one wishes. Even prefixes (and suffixes) can be factored out.
"Write-heavy" scenarios will probably be just fine with std::map (backed by an RB-tree) since the main downside of B-tree's is write amplification that isn't an issue since memory doesn't really have any block granularity.
LSM tree's in-memory will probably not be that useful as scanning becomes much more complicates (it's an interesting structure though if you have append-only workloads and want to implement dictionary for size-coded projects on top of a list).
You have to consolidate when the time has come to reclaim space and to avoid needless repeat compute during accesses. Might as well use it to run full LSM tactics. Especially when keeping in mind that array mapped trees have very simple index arithmetic once you treat them as semantically literally identical to a sorted (SoA) array with a cache-benefitting address/index scrambler.
B-trees algorithm requires leaf nodes to be filled up to some prespecified fill factor, usually from 50% to 70%. This is not compact by any measures.
Both LSM trees and COLA allow for much more compact storage. They also pretty cache friendly in the "cache oblivious" sense.
B-tree fill factors are a parameter that can be tuned to avoid extra splits depending on your insertion patterns, an in-memory variant doesn't need to be tuned like a disk-based variation.
Also nothing preventing the "bottom" of an LSM variation to be a dense B-tree like structure that just gets less updates.
The COLA paper also never mentions threading, an in-memory B-tree should scale better with size if there is multi-threading while I don't see an easy way to avoid big locks with COLA, maybe why the COLA paper was from 2000 and we haven't seen much additional development on it? (LSM-tree's work beautifully of course but then you basically have the double-space issue like with semi-space garbage collectors).
In the end, what you choose is dependent on your application and patterns, COLA is a clever structure that probably shines in some scenarios.
Like my scenario was a mostly heavy on consecutive insertions as well as lookups of potentially arbitrary compound keys, perfect for cola like since those are cheap.
> while I don't see an easy way to avoid big locks with COLA
Extension of COLA called Fractal Indexes (on-disk storage) are commercialized by Tokutek: https://en.wikipedia.org/wiki/Fractal_tree_index
For example, if you represent a set of values as an ordered array, you can perform many set operations with the (array) merge algorithm, which is cache oblivious one. You can avoid pointer chasing, etc, but your structure becomes static instead of dynamic as with, say, red-black trees. This is already a win because you can save memory and compute if at least one of your sets does not change much.
But, if you apply logarithmic method [1] you can have dynamic data structure (over static one, a sorted array) and still perform most of operations without pointer chasing and with cache oblivious merging.
[1] https://www.scilit.com/publications/4dd8074c2d05ecc9ed96b5cf...
LSM allow for very compact data representation because most levels of the tree do not change much through time, and this is what we are talking about here. This compact representation makes LSM trees faster at sequential reads too (less pointer chasing).
Also, you can differently construct LSM trees for different operations: higher LSM tree with more narrow levels allows for faster writes, flatter LSM tree with less but wider levels allow for faster reads.