Frequency Buckets (O(1) LFU Core)

What It Is

Bucketed LFU keeps entries grouped by frequency, with O(1) promotion and O(1) eviction using min_freq.

Generalized DS:

• A slot arena of entries (EntryId)
• For each freq, an intrusive list of entry ids (usually LRU within the bucket)
• A way to find the “current minimum non-empty frequency”

Core Types

• entries: Vec<Option<EntryMeta>>
• index: HashMap<K, EntryId>
• buckets: HashMap<u64, BucketMeta>
• min_freq: u64

Where BucketMeta holds:

• list_head/list_tail (intrusive list of EntryId)
• optional prev/next links between buckets to skip empty buckets quickly

Operations

touch(id)

• Remove id from freq bucket list.
• Increment freq.
• Insert into new bucket list head.
• If old bucket empty and was min_freq, advance min_freq.

evict()

• Choose victim from min_freq bucket tail (LRU tie-break).
• Remove from index + entry slots.

Notes

• The hard part is efficiently skipping empty frequencies. Linking buckets (prev/next) is one approach; scanning is another (but can become O(n)).
• Be explicit about saturation/overflow behavior (u64 counts can grow without bound; aging/decay is a separate concern).