  Consider two ordered positive real number arrays of equal size. The problem
is to find such set of indices of given size that the ratio of the sums of the
array elements with those indices is minimized. In this work, in order to
mitigate the exponential complexity of the brute force search, we present a
greedy algorithm applied to the search of such an index set. The main result of
the paper is the theorem that states that the algorithm eliminates from
candidates all index sets that do not contain any elements from the greedily
selected set. We additionally prove exactness for a particular case of a ratio
of the sums of only two elements.
