 The closure problem takes as input a directed acyclic graph with weights on its vertices and seeks the minimum ( or maximum ) weight of a closure , a set of vertices with no outgoing edges . ( The problem may be formulated for directed graphs without the assumption of acyclicity , but with no greater generality , because in this case it is equivalent to the same problem on the condensation of the graph . ) It may be solved in polynomial time using a reduction to the maximum flow problem . 
 The closure problem <a href='uninflect' title='1'><mark>takes</mark></a> as input a directed acyclic graph with weights on its vertices and <a href='uninflect' title='2'><mark>seeks</mark></a> the minimum ( or maximum ) weight of a closure , a set of vertices with no outgoing edges . ( The problem may be formulated for directed graphs without the assumption of acyclicity , but with no greater generality , because in this case it <a href='drop_aux' title='3'><mark>is</mark></a>equivalent to the same problem on the condensation of the graph . ) It may be solved in polynomial time using a reduction to the maximum flow problem . 
The closure problem take as input a directed acyclic graph w weights on its vertices and seek the minimum ( or maximum ) weight of a closure , a set of vertices witw outgoing edges . ( The problem may b formulated fir directed graphs w/o the assumption of acyclicity , but with no greater generality , b/c in this case it equivalent to the same problem on the condensation of da graph . ) It may be solved in polynomial time using a reduction to tdamaximum flow problem .