, Volume 17, Issue 2, pp 215234
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 Title
 Efficient construction of a small hitting set for combinatorial rectangles in high dimension
 Journal

Combinatorica
Volume 17, Issue 2 , pp 215234
 Cover Date
 199706
 DOI
 10.1007/BF01200907
 Print ISSN
 02099683
 Online ISSN
 14396912
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 068Q25
 05B40
 68R05
 Industry Sectors
 Authors

 Nathan Linial ^{(1)}
 Michael Luby ^{(2)}
 Michael Saks ^{(3)}
 David Zuckerman ^{(4)}
 Author Affiliations

 1. Computer Science Department, Hebrew University, Jerusalem, Israel
 2. DEC/SRC, 130 Lytton Avenue, 94301, Palo Alto, California
 3. Department of Mathematics, Rutgers University, 08854, New Brunswick, NJ, USA
 4. Department of Computer Sciences, The University of Texas at Austin, 78713, Austin, Texas, USA