On the Power of Additive Combinatorial Search Model

  • Vladimir Grebinski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)


We consider two generic problems of combinatorial search under the additive model. The first one is the problem of reconstructing bounded-weight vectors. We establish an optimal upper bound and observe that it unifies many known results for coin-weighing problems. The developed technique provides a basis for the graph reconstruction problem. Optimal upper bound is proved for the class of k-degenerate graphs.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Alok Aggarwal, Don Coppersmith, and Dan Kleitman. A generalized model for understanding evasiveness. Information Processing Letters, 30:205–208, 1989.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Martin Aigner. Combinatorial Search. John Wiley & Sons, 1988.Google Scholar
  3. [3]
    Noga Alon. Separating matrices. private communication, May 1997.Google Scholar
  4. [4]
    Noga Alon and Joel Spencer. The Probabilistic Method. John Wiley & Sons, 1992.Google Scholar
  5. [5]
    Béla Bollobás. Extremal Graph Theory. Academic Press, 1978.Google Scholar
  6. [6]
    Ding-Zhu Du and Frank K. Hwang. Combinatorial Group Testing and its applications, volume 3 of Series on applied mathematics. World Scientific, 1993.Google Scholar
  7. [7]
    Paul Erdős and Joel Spencer. Probabilistic Methods in Combinatorics. 1974.Google Scholar
  8. [8]
    Vladimir Grebinski and Gregory Kucherov. Optimal query bounds for reconstructing a hamiltonian cycle in complete graphs. In Proceedings of the 5th Israeli Symposium on Theory of Computing and Systems, pages 166–173. IEEE Press, 1997.Google Scholar
  9. [9]
    Vladimir Grebinski and Gregory Kucherov. Optimal reconstruction of graphs under the additive model. In Rainer Burkard and Gerhard Woeginger, editors, Algorithms — ESA’97, volume 1284 of LNCS, pages 246–258. Springer, 1997.Google Scholar
  10. [10]
    Bernt Lindström. On Möbius functions and a problem in combinatorial number theory. Canad. Math. Bull., 14(4):513–516, 1971.zbMATHMathSciNetGoogle Scholar
  11. [11]
    Bernt Lindström. Determining subsets by unramified experiments. In J.N. Srivastava, editor, A Survey of Statistical Designs and Linear Models, pages 407–418. North Holland, Amsterdam, 1975.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Vladimir Grebinski
    • 1
  1. 1.INRIA-LorrainneVillers-lès-NancyFrance

Personalised recommendations