, Volume 17, Issue 2, pp 215-234

First online:

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

  • Nathan LinialAffiliated withComputer Science Department, Hebrew University
  • , Michael LubyAffiliated with
  • , Michael SaksAffiliated withDepartment of Mathematics, Rutgers University
  • , David ZuckermanAffiliated withDepartment of Computer Sciences, The University of Texas at Austin

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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 formR 1×R 2×...×R d of size at least ∈m d . 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