Section: New Results

Algorithms and analysis

Participant : Laurent Alonso.

The Majority Problem

Given a set of $n$ elements each of which is either red or blue, Boyer and Moore's algorithm uses pairwise equal/not equal color comparisons to determine the majority color. We analyze the average behavior of their algorithm, proving that if all $2^n$ possible inputs are equally likely, the average number of color comparisons used is $n-\sqrt{2n/\pi }+O\left(1\right)$ and has variance $\frac{\pi -2}{\pi }n-\frac{\sqrt{2n}}{\sqrt{\pi }}+O\left(1\right)$. This joint work with Edward M. Reingold was published in the IPL journal [8] .

The $X+Y$ Sorting Problem

Some combinatorial approaches were taken to try to find bounds on the $X+Y$ problem: Given two lists: $X=(x_1,...,x_n)$, $Y=(y_1,...,y_m)$, determine the ordering of the values $x_i+y_j$ for $i\in [1,n],j\in [1,m]$.