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.
Similar content being viewed by others
References
D. Angluin, andL. G. Valiant: Fast probabilistic algorithms for Hamiltonian circuits and matchings,Journal of Computer and System Sciences,19, 155–193.
B. Bollobás:Extremal Graph theory, Chapter VIII., Academic Press, 1978.
P. A. Catlin: Subgraphs of graphs I.,Discrete Math. 10 (1974), 225–233.
H. Chernoff: A measure of asymptotic effiency for tests of a hypothesis based on the sum of observations,Annals of Math. Stat.,23 (1952), 493–509.
V. King: An Ω(n 5/4) lower bound on the randomized complexity of graph properties,Combinatorica,11 (1) (1991), 47–56.
J. Kahn, M. Saks, andD. Sturtevant: A topological aproach to evasiveness,Combinatorica,4(4) (1984), 297–306.
L. Lovász:Combinatorial Problems and Exercises, North-Holland 1979.
A. L. Rosenberg: On the time required to recognize properties of graphs: A problem,SIGACT News,5 (4) (1973), 15–16.
R. Rivest, andJ. Vuillemin: A generalization and proof of the Aanderaa-Rosenberg conjecture,Proc. 7th SIGACT Conference, (1975), ACM 1976.
N. Sauer, andJ. Spencer: Edge-disjoint replacement of graphs,J. of Combinatorial Theory Ser. B25 (1978), 295–302.
A. Yao: Probabilistic computation: towards a unified measure of complexity,Proc. 18th IEEE FOCS, 1977, pp. 222–227.
A. Yao: Lower bounds to randomized algorithms for graph properties,Proc. 28th IEEE FOCS, 1987, pp. 393–400.
Author information
Authors and Affiliations
Additional information
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.