3 ms·
Tweak the game a bit and it could become NP hard?
by gradschoolfail 5y ago
Tweak the game a bit and it could become NP hard?
- jamessb 5y agoIf you know the graph is planar, then you can find the Tutte embedding by solving a set of linear equations [1]. However, the problem of finding a drawing that minimises the number of edge crossings (or even just the number of crossings in such a layout [e.g., 2]) for a general graph is NP-hard. [1]: https://en.wikipedia.org/wiki/Tutte_embedding https://en.wikipedia.org/wiki/Tutte_embedding [2]: https://epubs.siam.org/doi/abs/10.1137/120872310 https://epubs.siam.org/doi/abs/10.1137/120872310
- ColinWright 5y agoThere are linear time algorithms that take a planar graph and find an embedding where all the edges are straight lines. However, I believe the problem of starting with a general graph and finding an embedding with the minimum number of edge crossings is NP-Hard.