So long as you're measuring in kilometers, as the bird flies. If you're talking about the distance a car would have to drive... okay, you're correct that it'd b

So long as you're measuring in kilometers, as the bird flies. If you're talking about the distance a car would have to drive... okay, you're correct that it'd be possible to drive through C and thereby cut down on cost, but that's somewhat besides the point. The algorithm this article is talking about assumes that all points are on an Euclidean map, and the distance between them is simply the Euclidean distance. This requires the triangle inequality to hold for straight lines, and allows optimizations based on that assumption. The inequality in itself is a weaker statement than saying the whole thing is euclidean, and I haven't read it carefully enough to be sure which is required, but any violation of it is necessarily a violation of the assumptions that make this heuristic work.