Question

I have this simple graph:

name -> string
 ^
 |
 v
label

let matrix = [|
[|false; false; false |];  
[|true; false; true  |];
[|false; true; false|] |]

(* compute transitive closure of matrix*)
let transClosure m =
  let n = Array.length m in
  for k = 0 to n - 1 do
    let mk = m.(k) in
    for i = 0 to n - 1 do
      let mi = m.(i) in
      for j = 0 to n - 1 do
    mi.(j) <- max mi.(j) (min mi.(k) mk.(j))
      done;
    done;
  done;
  m;;

output of transitive closure matrix is:

false false false
true true true
true true true

function compare equivalence classes:

let cmp_classes m i j =
  match m.(i).(j), m.(j).(i) with
      (* same class: there is a path between i and j, and between j and i *)
    | true, true -> 0
      (* there is a path between i and j *)
    | true, false -> -1
      (* there is a path between j and i *)
    | false, true -> 1
      (* i and j are not compareable *)
    | false, false -> raise Not_found

let sort_eq_classes m = List.sort (cmp_classes m);;

functions compute equivalence classes:

let eq_class m i =
  let column = m.(i)
  and set = ref [] in
  Array.iteri begin fun j _ ->
    if j = i || column.(j) && m.(j).(i) then
      set := j :: !set
  end column;
  !set;;

let eq_classes m =
  let classes = ref [] in
  Array.iteri begin fun e _ ->
    if not (List.exists (List.mem e) !classes) then
      classes := eq_class m e :: !classes
  end m;
  !classes;;

(* compute transitive closure of given matrix *)
let tc_xsds = transClosure matrix
(* finding equivalence classes in transitive closure matrix *)
let eq_xsds = eq_classes tc_xsds
(* sorting all equivalence classes with transitive closure matrix *)
let sort_eq_xsds = sort_eq_classes tc_xsds (List.flatten eq_xsds)

it gives me the order: label, name, string , mean correct order.

The problem is that, when I test with another graph, for example:

name -> string
 ^
 |
 v
label -> int

or

name -> int
^   \
|    \
v     v
label string

or

name -> string
|
v
label -> int

the output is raise Not_found

Could you please help me to explain why it cannot give the right order? Thank you.

Answer 1

As I said in previous thread, it cannot give you the right order because in some cases there are a lot of right orders.

In all three counterexamples, what would you expect regarding the order of string and int? One after another or just a random order? Since there is no edge between them, they are not comparable and your code raises Not_found exception.

One way to deal with this problem is catching Not_found exception, and saying that there’s no unique order. Or an gentler way is just returning 0 instead of raising exception which means you don’t care about the order between incomparable classes.

As @ygrek said in the comment, using a built-in exception is a bad idea. You should define a custom exception dedicated to your purpose.