An Ω(n 4/3) lower bound on the randomized complexity of graph properties

Abstract

We improve King's Ω(n 5/4) lower bound on the randomized decision tree complexity of monotone graph properties to Ω(n 4/3). The proof follows Yao's approach and improves it in a different direction from King's. At the heart of the proof are a duality argument combined with a new packing lemma for bipartite graphs.

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The paper was written while the author was a graduate student at the University of Chicago and was completed at M.I.T. The work was supported in part by NSF under GRANT number NSF 5-27561, the Air Force under Contract OSR-86-0076 and by DIMACS (Center for Discret Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center-NSF-STC88-09648.

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Hajnal, P. An Ω(n 4/3) lower bound on the randomized complexity of graph properties. Combinatorica 11, 131–143 (1991). https://doi.org/10.1007/BF01206357

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AMS subject classification code (1980)

  • 68 Q 15
  • 05 C 35
  • 05 C 80