Membership in Constant Time and Almost-Minimum Space

  • Authors:
  • Andrej Brodnik;J. Ian Munro

  • Affiliations:
  • -;-

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 1999

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Abstract

This paper deals with the problem of storing a subset of elements from the bounded universe $\mathcal{M} = \{0, \ldots, M-1\}$ so that membership queries can be performed efficiently. In particular, we introduce a data structure to represent a subset of $N$ elements of $\mathcal{M}$ in a number of bits close to the information-theoretic minimum, $B = \left\lceil \lg {M\choose N} \right\rceil$, and use the structure to answer membership queries in constant time.