Aging / Decayed LFU (Design Patterns)

LFU without aging tends to accumulate “historical winners” that stop being relevant.

Below are common, implementable aging strategies.

1) Periodic Global Decay (Halving)

Every T seconds (or every N accesses), apply:

• freq[key] = max(1, freq[key] / 2)

Tradeoffs:

• Simple conceptually.
• Naively O(n) per decay tick; must be infrequent or amortized.

Amortization approaches:

• Do decay in the background (careful with locks).
• Apply “lazy decay” by storing (freq, epoch) and adjusting when touched.

2) Epoch-Based Lazy Decay

Store per-entry:

• freq: u32
• last_epoch: u32 Global:
• epoch: u32 increments periodically

On access:

• apply decay based on epoch - last_epoch (e.g., shift right by delta)
• then increment and set last_epoch = epoch

Tradeoffs:

• Keeps hot path O(1)
• Requires deciding how decay maps from epoch delta to a freq reduction

3) Windowed LFU (Count-Min Sketch + Window)

For very large keyspaces (web caches), maintain approximate counts over a window:

• probabilistic counting to reduce memory
• eviction based on estimated frequency

Tradeoffs:

• Approximate; implementation complexity rises
• Good when exact per-key counters are too expensive

References

• Wikipedia: https://en.wikipedia.org/wiki/Cache_replacement_policies