Big Omicron and big Omega and big Theta

  title={Big Omicron and big Omega and big Theta},
  author={Donald Ervin Knuth},
  journal={SIGACT News},
  • D. Knuth
  • Published 1 April 1976
  • Computer Science
  • SIGACT News
Most of us have gotten accustomed to the idea of using the notation O(f(n)) to stand for any function whose magnitude is upper-bounded by a constant times f(n) , for all large n. Sometimes we also need a corresponding notation for lower-bounded functions, i.e., those functions which are at least as large as a constant times f(n) for all large n. Unfortunately~ people have occasionally been using the O-notation for lower bounds, for example when they reject a particular sorting method "because… Expand
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  • [1988] Proceedings. Structure in Complexity Theory Third Annual Conference
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Foreword This chapter is based on lecture notes from coding theory courses taught by Venkatesan
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  • Computer Science
  • Computer Science in Perspective
  • 2003
The elementary textbooks on algorithms and data structures have become too canonical too quickly, and that certain ways of presentation and also of selecting the contents are not as justified as they seem to be. Expand
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The goal of this chapter is to compute the Myerson value of cooperative games restricted by a combinatorial structure. There have been previous models developed to study the problem of games withExpand
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Let 0 be an irrational number, and a any number between 0 and 1 (0 included). Then it is well known that it is possible to find a sequence of positive integers w<i, n2, n3, ... such that (nr0) —>a asExpand
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  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1974
An algorithm is presented here which implies that every polynomial of degree n with at most s distinct coefficients can be realized with O(n/\log _s n) operations. Expand
II May
  • II May
  • 1976
IIardy, "Orders of Infinity,
  • Cambridge Tracts in Math. and Math. Physics,
  • 1924
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  • 1894