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I have about 100 atoms in a 3-D space. Each atom is a node. Edges are added between two nodes when they are closer than 0.32 nm with weight equals distance. I want to find a path from source node to destination node. Since the 100 atoms are not fully connected, sometimes I can't find a path.

What I want to do is to add one or more edges to make source and destination connected. Meanwhile, I also want to minimize the total weights of the new added edges. Again, weight is calculated from the two nodes' distance.

It is kind of a reverse problem of minimum cut. Is there any algorithm helps to do this?

Thanks a lot!

Ying Sheng
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1 Answers1

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It seems like one way would be to make use of a graph search algorithm for finding the shortest path, like Dijkstra's algorithm, and perhaps work from both ends (source and destination).

The only difference is that you can't know if any edge actually exists or not, and so you are creating the graph as you go. So if you start at A, and the nodes of the graph are A, B, C, D, E. Then you need to check if A-B, A-C, A-D, and A-E exists. If only A-B exists, then you check B-C, B-D, and B-E.

This will be O(|V|^2), but will really depend on how many edges get explored.

The same idea applies if you are only interested in adding edges that are longer than 0.32 nm. It's just that the path length calculation changes. Any edges that are less than .32 nm are zero-length, or simply a lot shorter (as they become less important). If that last bit doesn't work, then it gets a bit trickier.

Nuclearman
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