Big O Notation for Sysadmins

(Up-to-date source of this post.)

  • a mathematical way of describing scaling
  • used to classify a system based on how it responds to changes in input size
  • O is used because the growth rate of an algorithm's run-time is known as its order

Sub-linear scaling

  • O(1) - constant - no matter the scale of the input, performance of the system does not change (ex. hash-table lookup in RAM; such algorithms are rare)
  • O(log n) - logarithmic; ex. binary search grows slower as the size of the corpus being searched grows, but less then linearly

Linear scaling

  • O(n) linear - ex. twice as much data requires twice as much processing time

Super-linear scaling

  • O(n^m) - exponential - as input size grows the system slows down disproportionately
  • O(n^2) - quadratic (but everybody says exponential when they mean quadratic)


  • Practice of Cloud System Administration, Appendix C