[sltkr]

That code does NOT implement Prim's algorithm on a graph with randomly-weighted edges. Instead it just does a randomized breadth-first search of the area (starting from the corner), which is the same algorithm used for colouring, which is why the radial pattern occurs.

For a randomized spanning tree, edges should be generated with a random weight, and Prim's algorithm extracts them from the frontier ordered by weight. This creates a very different tree structure that is much more similar to the uniform spanning tree generated by Wilson's algorithm.

(This comment is based on the code from this page: http://bl.ocks.org/mbostock/11159599)

[mbostock]

I’d be happy if you could explain more, but the edges here are intentionally unweighted, so I believe the algorithm is correct. It’s based on the description here:

http://weblog.jamisbuck.org/2011/1/10/maze-generation-prim-s...

EDIT: Looks like you’re right! It makes a huge difference if you assign each edge a random weight once, rather than simply pulling a random edge of the frontier. Seems like the reference I used has this bug? Here is a fixed version:

http://bl.ocks.org/mbostock/11159599

[sltkr]

Yeah, I'm pretty sure the site you linked is wrong too, and I think the author doesn't realize it, because he says:

> My last post was about using Kruskal’s algorithm to generate random mazes. This article is about using another minimal spanning tree algorithm to do the same: Prim’s algorithm.

But his implementation is NOT the same! (His implementation of Kruskal's algorithm does look correct.) Extracting elements at a random index is not equivalent to assigning random weights to elements and extracting the minimum-weight elements.

[mbostock]

I spoke to Jamis Buck on Twitter. It’s called “Randomized Prim’s” on Wikipedia [1], but of course Wikipedia is not authoritative. It does seem confusing to call it a variant of Prim’s given how different the behavior is.

[1] http://en.wikipedia.org/wiki/Maze_generation_algorithm#Rando...

[sltkr]

I see -- apparently it's common to call this "Prim's algorithm" even though it is more accurately described as a randomized variant of breadth/depth-first search. Thanks for clarifying that.

I do still object to the text reading "This article is about using another minimal spanning tree algorithm to do the same" -- what is described there is not a minimal spanning tree algorithm (even if it's called Prim's algorithm).