Computing Graph Properties by Randomized Subcube Partitions

  • Ehud Friedgut
  • Jeff Kahn
  • Avi Wigderson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2483)


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.


Decision Tree Random Graph Threshold Probability Graph Property Decision Tree Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ehud Friedgut
    • 1
  • Jeff Kahn
    • 2
  • Avi Wigderson
    • 3
  1. 1.The Hebrew UniversityIsrael
  2. 2.Rutgers UniversityGermany
  3. 3.Institute for Advanced Study and The Hebrew UniversityIsrael

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