Having a complete bipartite graph with parts $A$ and $B$, which is edge-weighted, is there a way to compute a subgraph maximizing the sum of all its weights and:

1. Only a constant number $n$ of vertices from $A$ are used.
2. At most one edge points to each of the vertices in $B$.

In essence, which nodes from $A$ and which remaining edges to remove from the complete bipartite graph to get a graph with the maximum possible sum of its weights satisfying constraints 1 and 2.

In the example above, $n=2$ and $w_1 + w_2 + w_3$ is the maximum sum of weights which satisfies the two constraints.

Having a complete bipartite graph with parts $A$ and $B$, which is edge-weighted, is there a way to compute a subgraph with the maximum sum of all weights and:

1. Only a constant number $n$ of vertices from $A$ are used.
2. At most one edge points to each of the vertices in $B$.

In essence, which nodes from $A$ and which remaining edges to remove from the complete bipartite graph to get a graph with the maximum possible sum of its weights satisfying constraints 1 and 2.

In the example above, $n=2$ and $w_1 + w_2 + w_3$ is the maximum sum of weights which satisfies the two constraints.

Having a complete bipartite graph with parts $A$ and $B$, which is edge-weighted, is there a way to compute a subgraph maximizing the sum of all its weights and:

1. Only a constant number $n$ of vertices from $A$ are used.
2. An edge points to each of the vertices in $B$.

In essence, which nodes from $A$ and which remaining edges to remove from the complete bipartite graph to get a graph with the maximum possible sum of its weights satisfying constraints 1 and 2.

In the example above, $n=2$ and $w_1 + w_2 + w_3$ is the maximum sum of weights which satisfies the two constraints.

Having a complete bipartite graph with parts $A$ and $B$, which is edge-weighted, is there a way to compute a subgraph maximizing the sum of all its weights and:

1. Only a constant number $n$ of vertices from $A$ are used.
2. At most one edge points to each of the vertices in $B$.

In essence, which nodes from $A$ and which remaining edges to remove from the complete bipartite graph to get a graph with the maximum possible sum of its weights satisfying constraints 1 and 2.

In the example above, $n=2$ and $w_1 + w_2 + w_3$ is the maximum sum of weights which satisfies the two constraints.

Having a complete bipartite graph with parts $A$ and $B$, which is edge-weighted, is there a way to compute a maximum flow such that:

1. Only a constant number $n$ of vertices from $A$ are used.
2. An edge points to each of the vertices in $B$.

In essence, which nodes from $A$ and which remaining edges to remove from the complete bipartite graph to get a graph with the desired properties with a maximum possible sum of its weights.

In the example above, $n=2$ and $w_1 + w_2 + w_3$ is the maximum sum of weights which satisfies the two constraints.

Having a complete bipartite graph with parts $A$ and $B$, which is edge-weighted, is there a way to compute a subgraph maximizing the sum of all its weights and:

1. Only a constant number $n$ of vertices from $A$ are used.
2. An edge points to each of the vertices in $B$.

In essence, which nodes from $A$ and which remaining edges to remove from the complete bipartite graph to get a graph with the maximum possible sum of its weights satisfying constraints 1 and 2.

In the example above, $n=2$ and $w_1 + w_2 + w_3$ is the maximum sum of weights which satisfies the two constraints.