Shengyu Zhang

The Local Search problem, which finds a

local minimum of a black-box function on a given graph, is of both

practical and theoretical importance to many areas in computer

science and natural sciences. In this paper, we show that for the

Boolean hypercube $\B^n$, the randomized query complexity of Local

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Frederic Magniez, Ashwin Nayak, Miklos Santha, David Xiao

We consider the randomized decision tree complexity of the recursive 3-majority function. For evaluating a height $h$ formulae, we prove a lower bound for the $\delta$-two-sided-error randomized decision tree complexity of $(1-2\delta)(5/2)^h$, improving the lower bound of $(1-2\delta)(7/3)^h$ given by Jayram et al. (STOC '03). We also state a conjecture ... more >>>