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Questions about algorithms whose behaviour is determined not only by its input but also by a source of random numbers.

7
votes
Let's suppose that we have a polynomial time randomized algorithm $A$ for a decision problem $\Pi$ with the property that $$ \mathrm{Pr}[A \text{ is right}] > 1/2 $$ for all inputs. (In particular, i …
answered Nov 25 '13 by Louis
4
votes
In the paper, $h_Q$ isn't the height. It's the length of a random walk away from the root in a full binary tree (they insist every leaf is "nil"), so the expression they have is the right thing. Als …
answered Mar 15 '16 by Louis
4
votes
Since nobody else answered, here is what I had in mind when I made my comment. The basic idea behind the proposed amplification algorithm is that expanders are "negatively curved" in the sense that s …
answered Apr 10 '15 by Louis
11
votes
1answer
The usual simple algorithm for finding the median element in an array $A$ of $n$ numbers is: Sample $n^{3/4}$ elements from $A$ with replacement into $B$ Sort $B$ and find the rank $|B|\pm \sqrt{n}$ …
asked Apr 18 '12 by Louis
12
votes
Suppose your array has $n$ elements. As you have noted, the median is always in the bigger part after the first partition. The bigger part has size at most $\alpha n$ if the smaller part has size at …
answered Apr 18 '12 by Louis