Solving the smallest coverage between the bipartite graph are bipartite graph is an undirected graph, the directed graph can not be directly solved, require some special tools.
DAG point of minimum path coverage means that a simple path in a DAG disjoint less exhausted DAG cover all points (each point exactly once covered).
Solving method: set a the DAG, there are n points, increasing the n nodes, each split point x to x + n x and two-part, if there is a directed edge x-> y, is connected to an x-> y + n sides, so called a split point FIG bipartite graph. DAG minimum coverage path points = n - split point maximum matching of bipartite graph . Ask about the split point maximum matching of bipartite graphs can solve this problem.
Development: minimum path DAG repeatable point coverage, refers to a simple path in as few DAG can cover all of the intersecting points DAG (each covering at least one point).
Solution Method: Similar to cover the minimum point of the path of the DAG, for example, the path intersecting x-> p-> y and a-> p> b, two sides establish multiple x-> y and a-> b, of FIG. all such edges have this operation once, equivalent to seeking a transitive closure, split point and then find the maximum matching of the bipartite graph, and the minimum path back to the point of covering the same DAG.
Summary: DAG minimum path point coverage requirements split point corresponds to the maximum matching of the bipartite graph. DAG repeatable minimum path coverage point is equivalent to seeking a transitive closure (Floyd), a minimum path recalculation dots.
