{
  "tag": "DM95RK",
  "kind": "model",
  "slug": "word-ram",
  "name": "Word RAM",
  "aliases": [
    "word RAM model",
    "w-bit RAM"
  ],
  "area": "foundations/models-of-computation",
  "level": "core",
  "summary": "A RAM whose memory cells hold words of w bits, with w at least lg n, where arithmetic, comparison, bitwise and shift operations on words cost one step each.",
  "prereqs": [
    "random-access-machine",
    "unit-cost-model"
  ],
  "sources": [
    {
      "url": "https://en.wikipedia.org/wiki/Word_RAM",
      "locator": "article Word RAM"
    },
    {
      "book": "isbn:9780262046305",
      "title": "Cormen, Leiserson, Rivest and Stein, Introduction to Algorithms, fourth edition",
      "locator": "Section 2.2 (the RAM model and the word size c lg n)"
    },
    {
      "paper": "Michael L. Fredman and Dan E. Willard, Surpassing the information theoretic bound with fusion trees, Journal of Computer and System Sciences 47 (1993)",
      "locator": "the model and the transdichotomous assumption, and the sorting bound"
    },
    {
      "paper": "Michael L. Fredman and Dan E. Willard, Trans-dichotomous algorithms for minimum spanning trees and shortest paths, Journal of Computer and System Sciences 48 (1994)",
      "locator": "the introduction, where the term transdichotomous is defined"
    },
    {
      "paper": "Yijie Han and Mikkel Thorup, Integer sorting in O(n sqrt(log log n)) expected time and linear space, FOCS 2002",
      "locator": "abstract (the main result)"
    },
    {
      "paper": "Torben Hagerup, Sorting and searching on the word RAM, STACS 1998, Lecture Notes in Computer Science 1373",
      "locator": "the definition of the model and the survey of results"
    },
    {
      "paper": "Yijie Han, Deterministic sorting in O(n log log n) time and linear space, Journal of Algorithms 50 (2004)",
      "locator": "abstract (the main result)"
    },
    {
      "paper": "Peter van Emde Boas, Preserving order in a forest in less than logarithmic time and linear space, Information Processing Letters 6 (1977)",
      "locator": "the O(log log U) priority queue"
    },
    {
      "paper": "Dan E. Willard, Log-logarithmic worst-case range queries are possible in space Theta(N), Information Processing Letters 17 (1983)",
      "locator": "the y-fast trie"
    },
    {
      "paper": "Martin Dietzfelbinger, Torben Hagerup, Jyrki Katajainen and Martti Penttonen, A reliable randomized algorithm for the closest-pair problem, Journal of Algorithms 25 (1997)",
      "locator": "the multiply-shift hash family"
    },
    {
      "paper": "Arne Andersson, Torben Hagerup, Stefan Nilsson and Rajeev Raman, Sorting in linear time?, Journal of Computer and System Sciences 57 (1998)",
      "locator": "abstract (signature sort)"
    },
    {
      "paper": "Michael L. Fredman, Janos Komlos and Endre Szemeredi, Storing a sparse table with O(1) worst case access time, Journal of the ACM 31 (1984)",
      "locator": "abstract (the main result)"
    },
    {
      "paper": "Juris Hartmanis and Janos Simon, On the power of multiplication in random access machines, 15th Annual Symposium on Switching and Automata Theory (1974)",
      "locator": "abstract (the main result)"
    }
  ],
  "see_also": [
    "transdichotomous-model",
    "logarithmic-cost-model",
    "cell-probe-model",
    "pointer-machine",
    "real-ram",
    "integer-sorting",
    "predecessor-problem",
    "bit-parallelism"
  ],
  "url": "https://algorithm.tamnd.com/word-ram/",
  "path": "nodes/foundations/models-of-computation/word-ram",
  "status": {
    "slug": "word-ram",
    "h": {
      "level": 0,
      "max": 3,
      "label": "H0",
      "name": "no proof",
      "next": [
        "add a proof in proofs/ (06.5)"
      ]
    },
    "l": {
      "level": 0,
      "max": 4,
      "label": "L0",
      "name": "no Lean part",
      "next": [
        "name a Lean module in the lean field (07)"
      ]
    },
    "i": {},
    "v": {
      "level": 0,
      "max": 3,
      "label": "V0",
      "name": "none",
      "next": [
        "add viz/scene.ts or a figure (10)"
      ]
    },
    "w": {
      "level": 4,
      "max": 5,
      "label": "W4",
      "name": "complete",
      "next": [
        "a review of the text: no review record reviews/DM95RK/text.yaml"
      ]
    }
  },
  "scene": false
}