Re: [PATCH v3 2/2] memblock: use binary search to locate candidate regions

[tarunsahu@google.com]

sashiko-bot@kernel.org writes:

> Thank you for your contribution! Sashiko AI review found 1 potential issue(s) to consider:
> - [Medium] mm: commit message falsely claims O(N log N) worst-case complexity
> --
>
> commit ffd047af563941b5aabcd86a52d569f9b40c01ec
> Author: Tarun Sahu <tarunsahu@google.com>
>
> memblock: use binary search to locate candidate regions
>
> This commit introduces a binary search helper, memblock_bsearch_start(),
> to optimize finding candidate regions in memblock_add_range() and
> memblock_isolate_range(), aiming to reduce boot-time overhead during heavy
> memory fragmentation.
>
>> Under heavy memory fragmentation (such as KHO page preservation registering
>> hundreds of thousands of disjoint folios), scanning from index 0 on every
>> insertion and isolation results in O(N^2) complexity, causing boot-time
>> memory retrieval to take several minutes (~268s for 393k pages).
>>
>> Using binary search reduces the worst-case complexity to O(N log N)
>> (and O(N) for sequential appends), cutting KHO memory retrieval time
>> from ~268s to ~50ms.
>
> [Severity: Medium]
> Is the claim of O(N log N) worst-case complexity mathematically accurate here?
>
> While the binary search reduces the time to locate the insertion index to
> O(log N), the regions are still stored in a contiguous array. If disjoint
> memory regions are inserted in an order that requires inserting into the
> middle of the array, the subsequent elements still need to be shifted.
>
> Looking at memblock_insert_region() which is called during insertion:
>
> static void __init_memblock memblock_insert_region(...)
> {
>         ...
>         memmove(rgn + 1, rgn, (type->cnt - idx) * sizeof(*rgn));
>         ...
> }
>
> Because this memory move operation guarantees the worst-case complexity of a
> single insertion remains O(N), wouldn't inserting N disjoint regions in
> descending or scattered order still result in an O(N^2) worst-case time
> complexity overall?

Right. Here is the analysis below

KHO preserved regions is sorted in incremental order. So searching the candidate
is O(1) and insertion cost is O(1). So for N insertion is O(N).

for random regions, worst case (invertedly sorted)
Total Cost:
     Sum(log(i) + i, i=0, i=N)
     OlogN! + O(N(N+1)/2) ~ O (N^2)

hence, sashiko is right, So how can we improve this:  we cannot.

Incoming regions can overlap and there can be already present
regions in memblock_reserved array that might overlap with incoming
regions. So, only possible solution is one-by-by insertion. So here,
finding the location for insertion using binary search is best we can
do with linear arrays.

As KHO is the only user of having large reserved regions which are
sorted, Patch fulfils its purpose. I will update the commit msg to
correctly populate the time complexities.

~Tarun

>
> The described KHO workload sequentially appends regions, which avoids the
> shifting overhead and achieves O(N) overall. Could the commit message be
> updated to clarify that this patch improves sequential insertion to O(N),
> but the worst-case for fragmented insertions remains O(N^2) due to the array
> shifting?
>
> -- 
> Sashiko AI review · https://sashiko.dev/#/patchset/20260926092448.4090401-1-tarunsahu@google.com?part=2