Finding a subset of vectors with a coordinatewise large sum

Details Finding a subset of vectors with a coordinatewise large sum Finding a subset of vectors with a coordinatewise large sum

2012-01-13

arxiv.org/abs/1201.2880v2

Mathematics

Combinatorics

Scientific paper

Given a rational $\alpha=p/q$ and $N$ nonnegative $d$-dimensional real
vectors ${\bf e}_1$,..., ${\bf e}_N$, we show that it is always possible to
choose $(d-1)+\lceil (pN-d+1)/q\rceil$ of them such that their sum is
(componentwise) at least $(p/q)({\bf e}_1+...+{\bf e}_N)$. For fixed $d$ and
$\alpha$, this bound is sharp if $N$ is large enough.

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