Improved Lower Bounds on the Randomized Complexity of Graph Properties

  • Amit Chakrabarti
  • Subhash Khot
Conference paper

DOI: 10.1007/3-540-48224-5_24

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2076)
Cite this paper as:
Chakrabarti A., Khot S. (2001) Improved Lower Bounds on the Randomized Complexity of Graph Properties. In: Orejas F., Spirakis P.G., van Leeuwen J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg

Abstract

We prove a lower bound of Ω(n4/3 log1/3n) on the randomized decision tree complexity of any nontrivial monotone n-vertex bipartite graph property, thereby improving the previous bound of Ω(n4/3) due to Hajnal [H91]. Our proof works by improving a probabilistic argument in that paper, which also improves a graph packing lemma proved there. By a result of Gröger [G92] our complexity lower bound carries over from bipartite to general monotone n-vertex graph properties. Graph packing being a well-studied subject in its own right, our improved packing lemma and the probabilistic technique used to prove it, may be of independent interest.

Keywords

Decision tree complexity monotone graph properties randomized complexity randomized algorithms graph packing probabilistic method 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Amit Chakrabarti
    • 1
  • Subhash Khot
    • 1
  1. 1.Department of Computer SciencePrinceton UniversityPrincetonUSA

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