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Computing Graph Properties by Randomized Subcube Partitions

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Book cover Randomization and Approximation Techniques in Computer Science (RANDOM 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2483))

Abstract

We prove a new lower bound on the randomized decision tree complexity of monotone graph properties. For a monotone property A of graphs on n vertices, let p = p(A) denote the threshold probability of A, namely the value of p for which a random graph from G(n,p) has property A with probability 1/2. Then the expected number of queries made by any decision tree for A on such a random graph is at least Ω(n 2/ max{pn, logn}).

Our lower bound holds in the subcube partition model, which generalizes the decision tree model. The proof combines a simple combinatorial lemma on subcube partitions (which may be of independent interest) with simple graph packing arguments. Our approach motivates the study of packing of “typical” graphs, which may yield better lower bounds.

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References

  1. B. Bollobás, Extremal Graph Theory, Academic Press, Chapter 8, 1978.

    Google Scholar 

  2. P. A. Catlin, Subgraphs of graphs I, Discrete Math, 10, pp. 225–233, 1974.

    Google Scholar 

  3. A. Chakrabarti, S. Khot and Y. Shi, Evasiveness of subgraph containment and related properties, SIAM J. on Computing, 31, pp. 866–875, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Chakrabarti and S. Khot, Improved lower bounds on the randomized complexity of graph properties, Proc. of the 28th ICALP conference, Lecture Notes in Computer Science 2076, pp. 285–296, 2001.

    Google Scholar 

  5. D. H. Gröger, On the randomized complexity of monotone graph properties, Acta Cybernetica, 10, pp. 119–127, 1992.

    MATH  MathSciNet  Google Scholar 

  6. P. Hajnal, An Ω(n4/3) lower bound on the randomized complexity of graph properties, Combinatorica, 11, pp. 131–143, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  7. V. King, Lower bounds on the complexity of graph properties, Proc. of the 20th STOC conference, pp. 468–476, 1988.

    Google Scholar 

  8. J. Kahn, M. Saks and D. Sturtevant, A topological approach to evasiveness, Combinatorica 4, pp. 297–306, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  9. R. Rivest and J. Vuillemin, On recognizing graph properties from adjacency matrices, TCS 3, pp. 371–384, 1976.

    Article  MathSciNet  Google Scholar 

  10. N. Sauer and J. Spencer, Edge-disjoint placement of graphs, J. of Combinatorial Theory Ser. B, 25, pp. 295–302, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Saks and A. Wigderson, Probabilistic Boolean Decision Trees and the Complexity of Evaluating Game Trees, Proc. of the 27th FOCS conference, pp. 29–38, 1986.

    Google Scholar 

  12. J. von Neumann, Zur Theorie der Gesellschaftspiele, Matematische An-nalen, 100, pp. 295–320, 1928. English translation On the theory of games and strategy, in “Contributions to the theory of Games”, IV, pp.13-42, 1959.

    Article  MATH  Google Scholar 

  13. A.C. Yao, Lower bounds to randomized algorithms for graph properties, Proc. of the 28th FOCS conference, pp. 393–400, 1987.

    Google Scholar 

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Author information

Authors and Affiliations

  1. The Hebrew University, Israel

    Ehud Friedgut

  2. Rutgers University, Germany

    Jeff Kahn

  3. Institute for Advanced Study and The Hebrew University, Israel

    Avi Wigderson

Authors
  1. Ehud Friedgut
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  2. Jeff Kahn
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  3. Avi Wigderson
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Editor information

Editors and Affiliations

  1. Centre Universitaire d’Informatique, University of Geneva, 24, Rue Général Dufour, 1211, Genéve 4, Switzerland

    José D. P. Rolim

  2. Harvard University, DEAS, Maxwell Dworkin 337, 33 Oxford Street, Cambridge, MA, 02138, USA

    Salil Vadhan

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© 2002 Springer-Verlag Berlin Heidelberg

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Friedgut, E., Kahn, J., Wigderson, A. (2002). Computing Graph Properties by Randomized Subcube Partitions. In: Rolim, J.D.P., Vadhan, S. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 2002. Lecture Notes in Computer Science, vol 2483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45726-7_9

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  • DOI: https://doi.org/10.1007/3-540-45726-7_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44147-2

  • Online ISBN: 978-3-540-45726-8

  • eBook Packages: Springer Book Archive

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