given a set of n points in the plane and a set S of non ordered pairs of integers from 1 to n. if i label all the points with the numbers from 1 to n, i can considered the set S the edges of a graph. How can i efficiently found a labelling of the points such that the sum of the length of the edges is minimal?
2026-03-30 13:52:50.1774878770
labelling vertices in a graph in an optimal way problem
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In other words, you want to embed the graph in the plane, with each node corresponding to one of the specified points, in a way that minimizes the total edge length. This is an instance of the quadratic assignment problem. The flow for pairs in $S$ is $1$, and the flow for pairs of points not in $S$ is $0$.