# Network generation algorithm

I am trying to solve a network generation problem, and I'd be happy about inputs. First of all, my problem description:

I have a list of connections between locations with respective distances. For example:

``````LocationA <-> LocationB: 4500 m
LocationB <-> LocationC: 3000 m
LocationC <-> LocationA: 2000 m
...and so on...
``````

What I do not know, but try to find out: The actual geographic position of my locations. I do know the position of a few nodes in the network, and given a large list of connections with distances, I should be able to approximatively find the positions of my unknown locations.

Note: I am not trying to actually to optimize any paths within this network (e.g. Dijkstra etc.). I simply would like to know what geographic coordinates the nodes in my system have.

My question is: What sort of "node placement algorithm" am I looking for? I'd be happy for any keywords in this regard. I am 100% sure there are some algorithms for this problem, but I do not even know what to search for.

• Network connections consist of line segments (lines, polylines). You should be able to extract coordinates from the line segment nodes. – Matej Nov 11 '15 at 19:32
• When you say you know the positions of a few nodes, are you certain that the distance between two known nodes would exactly match a distance in your list, or only approximate it? – Kirk Kuykendall Nov 11 '15 at 21:38
• Thanks for commenting, guys. @Matej: Unfortunately, I do not have the lines in a shapefile or the like. I only have a csv-file which basically reads as A,B,4500 B,C,3000 C,A,2000 – Bob3k Nov 12 '15 at 13:06
• @Kirk: The distances are only approximately right. Judging from Felix' comment below, I would need 6 instead for 3 points for triangulation, right? – Bob3k Nov 12 '15 at 13:09
• Could this be classified as a computer vision/ pattern recognition problem? A camera captures an image, then generates points. A database of geometric objects is searched to find the the object whose nodes best match the points. – Kirk Kuykendall Nov 12 '15 at 17:08