  Consider a committee election consisting of (i) a set of candidates who are
divided into arbitrary groups each of size \emph{at most} two and a diversity
constraint that stipulates the selection of \emph{at least} one candidate from
each group and (ii) a set of voters who are divided into arbitrary populations
each approving \emph{at most} two candidates and a representation constraint
that stipulates the selection of \emph{at least} one candidate from each
population who has a non-null set of approved candidates.
  The DiRe (Diverse + Representative) committee feasibility problem (a.k.a. the
minimum vertex cover problem on unweighted undirected graphs) concerns the
determination of the smallest size committee that satisfies the given
constraints. Here, for this problem, we discover an unconditional deterministic
polynomial-time algorithm that is an amalgamation of maximum matching,
breadth-first search, maximal matching, and local minimization.
