Acta Informatica

, Volume 20, Issue 1, pp 103–111 | Cite as

On sets of Boolean n-vectors with all k-projections surjective

  • Ashok K. Chandra
  • Lawrence T. Kou
  • George Markowsky
  • Shmuel Zaks


Given a set, S, of Boolean n-vectors, one can choose k of the n coordinate positions and consider the set of k-vectors which results by keeping only the designated k positions of each vector, i.e., from k-projecting S. In this paper, we study the question of finding sets S as small as possible such that every k-projection of S yields all the 2 k possible k-vectors. We solve this problem constructively and almost optimally for k=2 and all n. For k≧3, the constructive solutions we describe are much larger than an O(k 2 k log n) nonconstructive upper bound which we derive. The nonconstructive approach allows us to generate fairly small sets S which have a very high probability of having the surjective k-projection property.


Information System Operating System Data Structure High Probability Communication Network 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Ashok K. Chandra
    • 1
  • Lawrence T. Kou
    • 2
  • George Markowsky
    • 1
  • Shmuel Zaks
    • 3
  1. 1.IBM Thomas J. Watson Research CenterYorktown HeightsUSA
  2. 2.Electrical and Computer Engineering DepartmentUniversity of CaliforniaDavisUSA
  3. 3.TechnionHaifaIsrael

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