Advertisement

Learning a Hidden Subgraph

  • Noga Alon
  • Vera Asodi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)

Abstract

We consider the problem of learning a labeled graph from a given family of graphs on n vertices in a model where the only allowed operation is to query whether a set of vertices induces an edge. Questions of this type are motivated by problems in molecular biology. In the deterministic nonadaptive setting, we prove nearly matching upper and lower bounds for the minimum possible number of queries required when the family is the family of all stars of a given size or all cliques of a given size. We further describe some bounds that apply to general graphs.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alon, N., Beigel, R., Kasif, S., Rudich, S., Sudakov, B.: Learning a Hidden Matching. In: Proceedings of the 43rd IEEE FOCS 2002, pp. 197–206 (2002)Google Scholar
  2. 2.
    Alon, N., Spencer, J.H.: The Probabilistic Method, 2nd edn. Wiley, New York (2000)zbMATHCrossRefGoogle Scholar
  3. 3.
    Bollobás, B.: Random Graphs. Academic Press, London (1985)zbMATHGoogle Scholar
  4. 4.
    Dyachkov, G., Rykov, V.V.: Bounds on the Length of Disjunctive Codes. Problemy Peredachi Informatsii 18(3), 158–166 (1982)MathSciNetGoogle Scholar
  5. 5.
    Grebinski, V., Kucherov, G.: Optimal Query Bounds for Reconstructing a Hamiltonian Cycle in Complete Graphs. In: Proc. 5th Israeli Symposium on Theoretical Computer Science, pp. 166–173 (1997)Google Scholar
  6. 6.
    Grebinski, V., Kucherov, G.: Reconstructing a Hamiltonian Cycle by Querying the Graph: Application to DNA Physical Mapping. Discrete Applied Math. 88, 147–165 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Grebinski, V., Kucherov, G.: Optimal Reconstruction of Graphs under the Additive Model. Algorithmica 28(1), 104–124 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Ruszinkó, M.: On the Upper Bound of the size of the r-cover-free families. Journal of Combinatorial Theory Series A 66(2), 302–310 (1994)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Noga Alon
    • 1
  • Vera Asodi
    • 2
  1. 1.Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Department of Computer Science, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

Personalised recommendations