cliques_to_jtree <- function(cliques, ns) {
  #  MK_JTREE Make an optimal junction tree.
  #  [jtree, root, B, w] = mk_jtree(cliques, ns)
  #  A junction tree is a tree that satisfies the jtree property, which says:
  #  for each pair of cliques U, V with intersection S, all cliques on the path between U and V
  #  contain S. (This ensures that local propagation leads to # global consistency.)
  #  We can create a junction tree by computing the maximal spanning tree of the junction graph.
  #  (The junction graph connects all cliques, and the weight of an edge (i, j) is
  #  |C(i) intersect C(j)|, where C(i) is the i'th clique.)
  #  The best jtree is the maximal spanning tree which minimizes the sum of the costs on each edge,
  #  where cost[i, j] <- w(C(i)) + w(C(j)), and w(C) is the weight of clique C,
  #  which is the total number of values C can take on.
  #  For details, see
  #   - Jensen and Jensen, "Optimal Junction Trees", UAI 94.
  #  Input:
  #   cliques{i} = nodes in clique i
  #   ns[i] <- number of values node i can take on
  #  Output:
  #   jtree[i, j] <- 1 iff cliques i and j aer connected
  #   root <- the clique that should be used as root
  #   B[i, j] <- 1 iff node j occurs in clique i
  #   w[i] <- weight of clique i

  num_cliques <- length(cliques)
  w <- zeros(num_cliques, 1)
  B <- zeros(num_cliques, 1)
  for (i in 1:num_cliques) {
    B[i, cliques[[i]]] <- 1
    w[i] <- prod(ns(cliques[[i]]))
  }

  #  C1[i, j] <- length(intersect(cliques{i}, cliques{j}))
  #  The length of the intersection of two sets is the dot product of their bit vector representation.
  C1 <- B %*% t(B)
  C1 <- setdiag(C1, 0)

  #  C2[i, j] <- w(i) + w(j)
  num_cliques <- length(w)
  W <- repmat(w, c(1, num_cliques))
  C2 <- W + t(W)
  C2 <- setdiag(C2, 0)

  jtree <- zeros(minimum_spanning_tree(-C1, C2))# Using - C1 gives * maximum * spanning tree

  #  The root is arbitrary, but since the first pass is towards the root,
  #  we would like this to correspond to going forward in time in a DBN.
  root <- num_cliques
  return(list("jtree" = jtree, "root" = root, "B" = B, "w" = w))
}