  Given a graph $G$, a non-negative integer $k$, and a weight function that
maps each vertex in $G$ to a positive real number, the \emph{Maximum Weighted
Budgeted Independent Set (MWBIS) problem} is about finding a maximum weighted
independent set in $G$ of cardinality at most $k$. A special case of MWBIS,
when the weight assigned to each vertex is equal to its degree in $G$, is
called the \emph{Maximum Independent Vertex Coverage (MIVC)} problem. In other
words, the MIVC problem is about finding an independent set of cardinality at
most $k$ with maximum coverage.
  Since it is a generalization of the well-known Maximum Weighted Independent
Set (MWIS) problem, MWBIS too does not have any constant factor polynomial time
approximation algorithm assuming $P \neq NP$. In this paper, we study MWBIS in
the context of bipartite graphs. We show that, unlike MWIS, the MIVC (and
thereby the MWBIS) problem in bipartite graphs is NP-hard. Then, we show that
the MWBIS problem admits a $\frac{1}{2}$-factor approximation algorithm in the
class of bipartite graphs, which matches the integrality gap of a natural LP
relaxation.
