{
  "slug": "lrfu",
  "term": "LRFU replacement",
  "aliases": [
    "LRFU",
    "Least Recently/Frequently Used"
  ],
  "definition": "LRFU is a block-replacement policy that combines reference frequency with recency through exponentially decaying scores.",
  "note": "For 0 <= lambda <= 1 and q = 2^(-lambda), each reference contributes q^(current tick - reference tick); the smallest total score is evicted. The clock advances once per block reference, not per second. Lambda = 0 gives frequency ordering, while lambda = 1 gives LRU ordering. [lee2001]\n\nA score and its last-reference tick suffice. On another reference after d ticks, update C to 1 + q^d C. Compare blocks at a common current tick, not by their stored scores from different times. The basic implementation initializes a fetched block's score, so history retention across eviction must be specified. [lee2001]\n\nExample: with two slots and requests A,A,A,B, consider C at tick 5. At q = 1/2, A scores 7/16 and B scores 1/2, so A is evicted. Comparing their stale stored values, 7/4 and 1, wrongly selects B. At q = 3/4, the aligned scores are 333/256 and 3/4, so B is evicted. These are exact constructed scores, not measured cache performance. [example]",
  "status": "research",
  "advantages": [],
  "limitations": [],
  "related": [
    "lru-replacement",
    "lru-k-replacement",
    "kosmo",
    "cache-pollution"
  ],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "updated": "2026-11-07",
  "citations": [
    {
      "id": "lee2001",
      "title": "Lee et al. LRFU: A Spectrum of Policies that Subsumes the Least Recently Used and Least Frequently Used Policies. IEEE TC 50(12), 2001, sections 3-4.",
      "url": "https://www.openu.ac.il/home/wiseman/2os/lru/lrfu.pdf",
      "accessed": "2026-11-07"
    },
    {
      "id": "metadata",
      "title": "University of Seoul publication record: LRFU, IEEE Transactions on Computers, 1352-1361. DOI 10.1109/TC.2001.970573.",
      "url": "https://pure.uos.ac.kr/en/publications/lrfu-a-spectrum-of-policies-that-subsumes-the-least-recently-used/",
      "accessed": "2026-11-07"
    },
    {
      "id": "example",
      "title": "Hesela: exact LRFU score alignment example (JSON).",
      "url": "https://hesela.dev/research/lrfu/example.json",
      "accessed": "2026-11-07"
    },
    {
      "id": "code",
      "title": "Hesela: exact rational score calculation (Python).",
      "url": "https://hesela.dev/research/lrfu/model.py",
      "accessed": "2026-11-07"
    }
  ],
  "provenance": [
    "Source review covers the base algorithm; correlated-reference masking and the optimized heap/list implementation are not reproduced. [lee2001]",
    "The constructed four-reference example uses equal-size blocks, an empty initial cache and exact rational arithmetic. It is not a reproduction of the paper's workload experiments. [code]"
  ]
}