, Volume 17, Issue 2, pp 215–234 | Cite as

Efficient construction of a small hitting set for combinatorial rectangles in high dimension

  • Nathan Linial
  • Michael Luby
  • Michael Saks
  • David Zuckerman


We describe a deterministic algorithm which, on input integersd, m and real number ∈∃ (0,1), produces a subset S of [m]d={1,2,3,...,m}d that hits every combinatorial rectangle in [m]d of volume at least ∈, i.e., every subset of [m]d the formR1×R2×...×Rd of size at least ∈md. The cardinality of S is polynomial inm(logd)/∈, and the time to construct it is polynomial inmd/∈. The construction of such sets has applications in derandomization methods based on small sample spaces for general multivalued random variables.

Mathematics Subject Classification (1991)

068Q25 05B40 68R05 


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Copyright information

© János Bolyai Mathematical Society 1997

Authors and Affiliations

  • Nathan Linial
    • 1
  • Michael Luby
    • 2
  • Michael Saks
    • 3
  • David Zuckerman
    • 4
  1. 1.Computer Science DepartmentHebrew UniversityJerusalemIsrael
  2. 2.Palo Alto
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickUSA
  4. 4.Department of Computer SciencesThe University of Texas at AustinAustinUSA

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