  Consider a problem where 4k given vectors need to be partitioned into k
clusters of four vectors each. A cluster of four vectors is called a quad, and
the cost of a quad is the sum of the component-wise maxima of the four vectors
in the quad. The problem is to partition the given 4k vectors into k quads with
minimum total cost. We analyze a straightforward matching-based algorithm, and
prove that this algorithm is a (3/2)-approximation algorithm for this problem.
We further analyze the performance of this algorithm on a hierarchy of special
cases of the problem, and prove that, in one particular case, the algorithm is
a (5/4)-approximation algorithm. Our analysis is tight in all cases except one.
