Is there a faster way to calculate the 2D Minimum Spanning Tree?


I’m implementing a MST for a set of 2D points, here is my current code using the Prim agorithm :

module IntSet = Set.Make (Int)

let prim_alg adj_matrix city_count =
  let eval a b = adj_matrix.(a).(b) in 
  let init_visited = IntSet.singleton 0 in
  let init_visit =
    let rec aux1 i acc =
      if i < city_count then aux1 (i + 1) (IntSet.add i acc) else acc
    aux1 1 IntSet.empty
  let rec aux to_visit visited score =
    if not @@ IntSet.is_empty to_visit then (
      let added = ref (-1) in
      let mini = ref max_int in
        (fun c1 ->
            (fun c2 ->
              let len = eval c1 c2 in
              if len < !mini then (
                mini := len;
                added := c1))
      let new_to_visit = IntSet.remove !added to_visit in
      let new_visited = IntSet.add !added visited in
      aux new_to_visit new_visited (score + !mini))
    else score
  aux init_visit init_visited 0

I don’t know if I can improve it programmatically or if someone already implemented a better algorithm for this in OCaml (I know some fancy one exist).

Ocamlgraph is the place to look for this kind of stuff.