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Asked: 2026-05-31T21:10:48+00:00

I would like to find a better algorithm to solve the following problem: There

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I would like to find a better algorithm to solve the following problem:

There are N starting points (purple) and N target points (green) in 2D. I want an algorithm that connects starting points to target points by a line segment (brown) without any of these segments intersecting (red) and while minimizing the cumulative length of all segments.

My first effort in C++ was permuting all possible states, find intersection-free states, and among those the state with minimum total segment length O(n!) . But I think there has to be a better way.

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Any idea? Or good keywords for search?

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1 Answer

  1. Editorial Team

    This is Minimum Euclidean Matching in 2D. The link contains a bibliography of what’s known about this problem. Given that you want to minimize the total length, the non-intersection constraint is redundant, as the length of any pair of segments that cross can be reduced by uncrossing them.

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