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2
votes
Maximum weighted matching in Bipartite Graph
You can turn the problem into an edge-weighted variant by setting the weight on edge $vu$ to be $\texttt{valueArray}(u)$ where $w(vu) = \texttt{valueArray}(u)$ is the value of $u \in U$.
Now a maximum …
5
votes
Accepted
Term for a matching which is perfect on one side only
Such a matching is said to saturate one of the sides. More specifically, if $M$ is a matching of a graph $G$ and $v$ is incident to one of the edges of $M$, we say that $M$ saturates $v$. If $A$ is …
1
vote
Dinitz’ algorithm in simple unit-capacity networks
I have no clue about how the values in the other two lemmas are brought up.
The how is this: What are the values $a$ and $b$ such that $ab = n$ and $O(a + b)$ is minimized?
The answer is $\sqrt n$, …