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Linear programming is the study of optimizing a linear function over a set of linear inequalities. The Simplex Method, Ellipsoid Method and Interior Point Method are popular algorithms to solve linear programs.
2
votes
Accepted
Find edge weights that fit given node weights
You can solve it by using maximum network flow: First you duplicate every vertex $i$, creating a twin $i'$, which inherits the same degree $d_{i'}:= d_i$. Each edge $ij$ becomes two edges $i,j'$ and $ …
2
votes
Complexity of a weirdo two-dimensional sorting problem
Here are some more cross-connections: The problem can be massaged into a least-squares matching problem
$$\sum_{p\in S} \|(-f(p))-p\|^2 \to \min$$ between $S$ and the grid rotated by $180^\circ$ (whic …