.

wcfs/internal/xbtree.py

@@ -223,7 +223,7 @@ def Restructure(ztree, newStructure):
     #
     #          sum min d(a,b)     sum min d(a,b)
     #          a∈A b∈B            b∈B a∈A
-    # D(A,B) = ──────────────  +  ──────────────
+    # D(A,B) = ──────────────  +  ──────────────        XXX
     #               N(A)              N(B)
     #
 
@@ -232,6 +232,35 @@ def Restructure(ztree, newStructure):
     # - bucket.next_bucket  will point to bucket that is coming with next keys in the tree
     tnew = newStructure.copy()
 
+    # assign assignes tree nodes from RNv to ztree nodes from RZv in optimal way.
+    # Bj ∈ RNv is mapped into Ai ∈ RZv such that that sum_j D(A_i, Bj) is minimal.
+    # it is used to associate nodes in tnew to ztree nodes.
+    def assign(RZv, RNv):
+        for rzn in RZv:
+            assert isinstance(rzn, _NodeInRange)
+            assert isinstance(rzn.node, (ztreeType, zbucketType))
+        for rn in RNv:
+            assert isinstance(rn, _NodeInRange)
+            assert isinstance(rn.node, (Tree|Bucket)
+
+        # prepare cost matrix
+        C = np.zeros((len(RNv), len(RZv)))
+        for j in range(RNv):        # "workers"
+            for i in range(RZv):    # "jobs"
+                C[j,i] = D(A[i], B[j])
+
+        # TODO try to avoid scipy dependency; we could also probably make
+        # assignments more efficiently taking that Av and Bv are key↑ and the
+        # property of D function so that if B2 > B1 (all keys in B2 > all keys
+        # in B1) and A < B1.hi, then D(B2, A) > D(B1, A).
+        jv, iv = scipy.optimize.linear_sum_assignment(C)
+
+        if len(Av) == len(Bv):
+            # XXX assert the result is 1-1 mapping
+
+        # XXX assert assignments are in key↑ order
+
+
     zrlevelv = list(__zwalkBFS(ztree))   # [] of _NodeInRange
     rlevelv  = list( __walkBFS(tnew))    # [] of _NodeInRange