Clean up magagement of blossom labels
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@ -386,7 +386,7 @@ class _Blossom:
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self.tree_edge: Optional[tuple[int, int]] = None
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# For a labeled top-level blossom,
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# "alternating_tree" is the set of all top-level blossoms that belong
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# "tree_blossoms" is the set of all top-level blossoms that belong
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# to the same alternating tree. The same set instance is shared by
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# all top-level blossoms in the tree.
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self.tree_blossoms: "Optional[set[_Blossom]]" = None
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@ -856,77 +856,155 @@ class _MatchingContext:
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return (-1, math.inf)
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#
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# General support routines:
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# Managing blossom labels:
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#
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# TODO -- Although this code is correct, there is a conceptual problem
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# that the division of responsibilities is asymmetric.
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# For example, assign_blossom_label_s is not the exact
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# opposite of remove_blossom_label_s, and remove_blossom_label_s
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# has different responsibilities from remove_blossom_label_t.
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# This must be fixed by shifting responsibilities or renaming
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# functions, otherwise this stuff is impossible to understand.
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def assign_blossom_label_s(self, blossom: _Blossom) -> None:
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"""Assign label S to an unlabeled top-level blossom."""
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"""Change an unlabeled top-level blossom into an S-blossom."""
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assert blossom.parent is None
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assert blossom.label == _LABEL_NONE
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blossom.label = _LABEL_S
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# Labeled blossoms must not be in the delta2 queue.
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self.delta2_disable_blossom(blossom)
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# Prepare for lazy updating of S-blossom dual variable.
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# Adjust for lazy updating of S-blossom dual variables.
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#
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# The true dual value of an unlabeled top-level blossom is
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# blossom.dual_var
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#
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# while the true dual value of a top-level S-blossom is
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# blossom.dual_var + ctx.delta_sum_2x
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#
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# The value of blossom.dual_var must be adjusted accordingly
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# when the blossom changes from unlabeled to S-blossom.
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#
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if isinstance(blossom, _NonTrivialBlossom):
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blossom.dual_var -= self.delta_sum_2x
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def remove_blossom_label_s(self, blossom: _Blossom) -> None:
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"""Remove label S from a top-level S-blossom."""
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assert blossom.parent is None
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assert blossom.label == _LABEL_S
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blossom.label = _LABEL_NONE
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# Catch up with lazy updates to S-blossom dual variable.
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if isinstance(blossom, _NonTrivialBlossom):
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blossom.dual_var += self.delta_sum_2x
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def assign_vertex_label_s(self, blossom: _Blossom) -> None:
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"""Adjust after assigning label S to previously unlabeled vertices."""
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# Add the new S-vertices to the scan queue.
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vertices = blossom.vertices()
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self.scan_queue.extend(vertices)
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# Prepare for lazy updating of S-vertex dual variables.
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# Apply pending updates to vertex dual variables and prepare
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# for lazy updating of S-vertex dual variables.
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#
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# For S-blossoms, blossom.vertex_dual_offset is always 0.
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#
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# Furthermore, the true dual value of an unlabeled vertex is
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# (vertex_dual_2x[x] + blossom.vertex_dual_offset) / 2
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#
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# while the true dual value of an S-vertex is
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# (vertex_dual_2x[x] - delta_sum_2x) / 2
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#
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# The value of vertex_dual_2x must be adjusted accordingly
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# when vertices change from unlabeled to S-vertex.
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#
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vertex_dual_fixup = self.delta_sum_2x + blossom.vertex_dual_offset
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blossom.vertex_dual_offset = 0
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vertices = blossom.vertices()
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for x in vertices:
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self.vertex_dual_2x[x] += vertex_dual_fixup
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# S-vertices do not keep track of potential delta2 edges.
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self.delta2_clear_vertex(x)
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# Add the new S-vertices to the scan queue.
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self.scan_queue.extend(vertices)
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def assign_blossom_label_t(self, blossom: _Blossom) -> None:
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"""Assign label T to an unlabeled top-level blossom."""
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"""Change an unlabeled top-level blossom into a T-blossom."""
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assert blossom.parent is None
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assert blossom.label == _LABEL_NONE
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blossom.label = _LABEL_T
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# Labeled blossoms must not be in the delta2 queue.
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self.delta2_disable_blossom(blossom)
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if isinstance(blossom, _NonTrivialBlossom):
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# Prepare for lazy updating of T-blossom dual variables.
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# Adjust for lazy updating of T-blossom dual variables.
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#
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# The true dual value of an unlabeled top-level blossom is
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# blossom.dual_var
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#
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# while the true dual value of a top-level T-blossom is
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# blossom.dual_var - ctx.delta_sum_2x
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#
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# The value of blossom.dual_var must be adjusted accordingly
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# when the blossom changes from unlabeled to S-blossom.
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#
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blossom.dual_var += self.delta_sum_2x
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# Insert blossom into the delta4 queue.
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# Top-level T-blossoms are tracked in the delta4 queue.
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assert blossom.delta4_node is None
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blossom.delta4_node = self.delta4_queue.insert(blossom.dual_var,
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blossom)
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# Prepare for lazy updating of T-vertex dual variables.
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#
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# The true dual value of an unlabeled vertex is
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# (vertex_dual_2x[x] + blossom.vertex_dual_offset) / 2
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#
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# while the true dual value of a T-vertex is
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# (vertex_dual_2x[x] + blossom.vertex_dual_offset + delta_sum_2x) / 2
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#
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# The value of blossom.vertex_dual_offset must be adjusted accordingly
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# when the blossom changes from unlabeled to T-blossom.
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#
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blossom.vertex_dual_offset -= self.delta_sum_2x
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def remove_blossom_label_s(self, blossom: _Blossom) -> None:
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"""Change a top-level S-blossom into an unlabeled blossom.
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For a blossom with "j" vertices and "k" incident edges,
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this function takes time O((j + k) * log(n)).
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This function is called at most once per blossom per stage.
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It therefore takes total time O((n + m) * log(n)) per stage.
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"""
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assert blossom.parent is None
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assert blossom.label == _LABEL_S
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blossom.label = _LABEL_NONE
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# Unwind lazy delta updates to the S-blossom dual variable.
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if isinstance(blossom, _NonTrivialBlossom):
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blossom.dual_var += self.delta_sum_2x
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assert blossom.vertex_dual_offset == 0
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vertex_dual_fixup = -self.delta_sum_2x
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edges = self.graph.edges
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adjacent_edges = self.graph.adjacent_edges
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for x in blossom.vertices():
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# Unwind lazy delta updates to S-vertex dual variables.
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self.vertex_dual_2x[x] += vertex_dual_fixup
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# Scan the incident edges of all vertices in the blossom.
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for e in adjacent_edges[x]:
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(p, q, _w) = edges[e]
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y = p if p != x else q
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# If this edge is in the delta3 queue, remove it.
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# Only edges between S-vertices are tracked for delta3,
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# and vertex "x" is no longer an S-vertex.
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self.delta3_remove_edge(e)
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by = self.vertex_set_node[y].find()
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if by.label == _LABEL_S:
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# Edge "e" connects unlabeled vertex "x" to S-vertex "y".
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# It must be tracked for delta2 via vertex "x".
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self.delta2_add_edge(e, x, blossom)
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else:
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# Edge "e" connects former S-vertex "x" to T-vertex
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# or unlabeled vertex "y". That implies this edge was
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# tracked for delta2 via vertex "y", but it must be
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# removed now.
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self.delta2_remove_edge(e, y, by)
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def remove_blossom_label_t(self, blossom: _Blossom) -> None:
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"""Remove label T from a top-level T-blossom."""
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"""Change a top-level T-blossom into an unlabeled blossom."""
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assert blossom.parent is None
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assert blossom.label == _LABEL_T
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@ -934,47 +1012,34 @@ class _MatchingContext:
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if isinstance(blossom, _NonTrivialBlossom):
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# Remove blossom from delta4 queue.
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# Unlabeled blossoms are not tracked in the delta4 queue.
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assert blossom.delta4_node is not None
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self.delta4_queue.delete(blossom.delta4_node)
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blossom.delta4_node = None
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# Unwind lazy updates to T-blossom dual variable.
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# Unwind lazy updates to the T-blossom dual variable.
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blossom.dual_var -= self.delta_sum_2x
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# Unwind lazy updates of T-vertex dual variables.
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blossom.vertex_dual_offset += self.delta_sum_2x
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def remove_vertex_label_s(self, x: int, bx: _Blossom) -> None:
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"""Adjust delta tracking for S-vertex losings its label.
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# Enable unlabeled top-level blossom for delta2 tracking.
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self.delta2_enable_blossom(blossom)
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This function is called when vertex "x" was an S-vertex but
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has just lost its label. This requires adjustments in the tracking
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of delta2 and delta3.
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def change_s_blossom_to_subblossom(self, blossom: _Blossom) -> None:
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"""Change a top-level S-blossom into an S-subblossom."""
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This function is takes time O(q * log(n)),
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where q is the number of incident edges of vertex "x".
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This function is called at most once per vertex per stage.
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This function therefore takes ammortized time O(m * log(n)) per stage.
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"""
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assert blossom.parent is None
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assert blossom.label == _LABEL_S
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blossom.label = _LABEL_NONE
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# Scan the edges that are incident on "x".
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edges = self.graph.edges
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for e in self.graph.adjacent_edges[x]:
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(p, q, _w) = edges[e]
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y = p if p != x else q
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# Unwind lazy delta updates to the S-blossom dual variable.
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if isinstance(blossom, _NonTrivialBlossom):
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blossom.dual_var += self.delta_sum_2x
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self.delta3_remove_edge(e)
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by = self.vertex_set_node[y].find()
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if by.label == _LABEL_S:
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# This is an edge between "x" and an S-vertex.
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# Add this edge to "vertex_sedge_queue[x]".
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# Update delta2 tracking accordingly.
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self.delta2_add_edge(e, x, bx)
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else:
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self.delta2_remove_edge(e, y, by)
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#
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# General support routines:
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#
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def reset_blossom_label(self, blossom: _Blossom) -> None:
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"""Remove blossom label."""
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@ -983,27 +1048,9 @@ class _MatchingContext:
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assert blossom.label != _LABEL_NONE
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if blossom.label == _LABEL_S:
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# Remove label.
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blossom.label = _LABEL_NONE
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# Unwind lazy delta updates to S-blossom dual variable.
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if isinstance(blossom, _NonTrivialBlossom):
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blossom.dual_var += self.delta_sum_2x
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# Unwind lazy delta updates to S-vertex dual variables.
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assert blossom.vertex_dual_offset == 0
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vertex_dual_fixup = -self.delta_sum_2x
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for x in blossom.vertices():
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self.vertex_dual_2x[x] += vertex_dual_fixup
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# Adjust delta tracking for S-vertex losing its label.
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self.remove_vertex_label_s(x, blossom)
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self.remove_blossom_label_s(blossom)
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elif blossom.label == _LABEL_T:
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self.remove_blossom_label_t(blossom)
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self.delta2_enable_blossom(blossom)
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def _check_alternating_tree_consistency(self) -> None:
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"""TODO -- remove this function, only for debugging"""
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@ -1155,25 +1202,28 @@ class _MatchingContext:
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# Remove blossom labels.
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# Mark vertices inside former T-blossoms as S-vertices.
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for sub in subblossoms:
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if sub.label == _LABEL_S:
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self.remove_blossom_label_s(sub)
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elif sub.label == _LABEL_T:
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if sub.label == _LABEL_T:
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self.remove_blossom_label_t(sub)
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self.assign_vertex_label_s(sub)
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self.assign_blossom_label_s(sub)
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self.change_s_blossom_to_subblossom(sub)
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# Create the new blossom object.
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blossom = _NonTrivialBlossom(subblossoms, path.edges)
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# Assign label S to the new blossom and link it to the tree.
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self.assign_blossom_label_s(blossom)
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# Assign label S to the new blossom.
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blossom.label = _LABEL_S
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# Prepare for lazy updating of S-blossom dual variable.
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blossom.dual_var = -self.delta_sum_2x
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# Link the new blossom to the alternating tree.
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tree_blossoms = subblossoms[0].tree_blossoms
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assert tree_blossoms is not None
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blossom.tree_edge = subblossoms[0].tree_edge
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blossom.tree_blossoms = tree_blossoms
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tree_blossoms.add(blossom)
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# Insert into the blossom array.
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# Add to the list of blossoms.
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self.nontrivial_blossom.add(blossom)
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# Link the subblossoms to the their new parent.
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@ -1215,6 +1265,38 @@ class _MatchingContext:
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return (nodes, edges)
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def expand_unlabeled_blossom(self, blossom: _NonTrivialBlossom) -> None:
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"""Expand the specified unlabeled blossom.
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This function takes total time O(n*log(n)) per stage.
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"""
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assert blossom.parent is None
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assert blossom.label == _LABEL_NONE
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# Remove blossom from the delta2 queue.
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self.delta2_disable_blossom(blossom)
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# Split union-find structure.
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blossom.vertex_set.split()
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# Prepare to push lazy delta updates down to the sub-blossoms.
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vertex_dual_offset = blossom.vertex_dual_offset
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blossom.vertex_dual_offset = 0
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# Convert sub-blossoms into top-level blossoms.
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for sub in blossom.subblossoms:
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assert sub.label == _LABEL_NONE
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sub.parent = None
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assert sub.vertex_dual_offset == 0
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sub.vertex_dual_offset = vertex_dual_offset
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self.delta2_enable_blossom(sub)
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# Delete the expanded blossom.
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self.nontrivial_blossom.remove(blossom)
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def expand_t_blossom(self, blossom: _NonTrivialBlossom) -> None:
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"""Expand the specified T-blossom.
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@ -1225,34 +1307,18 @@ class _MatchingContext:
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assert blossom.label == _LABEL_T
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assert blossom.delta2_node is None
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# Remove expanded blossom from the delta4 queue.
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assert blossom.delta4_node is not None
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self.delta4_queue.delete(blossom.delta4_node)
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blossom.delta4_node = None
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# Remove blossom from its alternating tree.
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tree_blossoms = blossom.tree_blossoms
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assert tree_blossoms is not None
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tree_blossoms.remove(blossom)
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# Split union-find structure.
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blossom.vertex_set.split()
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# Remove label T.
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self.remove_blossom_label_t(blossom)
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# Prepare to push lazy delta updates down to the sub-blossoms.
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vertex_dual_fixup = self.delta_sum_2x + blossom.vertex_dual_offset
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blossom.vertex_dual_offset = 0
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# Expand the now-unlabeled blossom.
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self.expand_unlabeled_blossom(blossom)
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# Convert sub-blossoms into top-level blossoms.
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for sub in blossom.subblossoms:
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assert sub.label == _LABEL_NONE
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sub.parent = None
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assert sub.vertex_dual_offset == 0
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sub.vertex_dual_offset = vertex_dual_fixup
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self.delta2_enable_blossom(sub)
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# The expanding blossom was part of an alternating tree, linked to
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# The expanded blossom was part of an alternating tree, linked to
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# a parent node in the tree via one of its subblossoms, and linked to
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# a child node of the tree via the base vertex.
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# We must reconstruct this part of the alternating tree, which will
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@ -1296,40 +1362,6 @@ class _MatchingContext:
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sub.tree_blossoms = tree_blossoms
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tree_blossoms.add(sub)
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# Delete the expanded blossom.
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self.nontrivial_blossom.remove(blossom)
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def expand_unlabeled_blossom(self, blossom: _NonTrivialBlossom) -> None:
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"""Expand the specified unlabeled blossom.
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This function takes total time O(n*log(n)) per stage.
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"""
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assert blossom.parent is None
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assert blossom.label == _LABEL_NONE
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self.delta2_disable_blossom(blossom)
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# Split union-find structure.
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blossom.vertex_set.split()
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# Prepare to push lazy delta updates down to the sub-blossoms.
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vertex_dual_offset = blossom.vertex_dual_offset
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blossom.vertex_dual_offset = 0
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# Convert sub-blossoms into top-level blossoms.
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for sub in blossom.subblossoms:
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assert sub.label == _LABEL_NONE
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sub.parent = None
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assert sub.vertex_dual_offset == 0
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sub.vertex_dual_offset = vertex_dual_offset
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||||
self.delta2_enable_blossom(sub)
|
||||
|
||||
# Delete the expanded blossom.
|
||||
self.nontrivial_blossom.remove(blossom)
|
||||
|
||||
#
|
||||
# Augmenting:
|
||||
#
|
||||
|
|
@ -1492,7 +1524,6 @@ class _MatchingContext:
|
|||
# Assign label S to the blossom that contains vertex "x".
|
||||
bx = self.vertex_set_node[x].find()
|
||||
self.assign_blossom_label_s(bx)
|
||||
self.assign_vertex_label_s(bx)
|
||||
|
||||
y = self.vertex_mate[x]
|
||||
if y == -1:
|
||||
|
|
@ -1712,7 +1743,6 @@ class _MatchingContext:
|
|||
|
||||
# Assign label S.
|
||||
self.assign_blossom_label_s(bx)
|
||||
self.assign_vertex_label_s(bx)
|
||||
|
||||
# Mark blossom as the root of an alternating tree.
|
||||
bx.tree_edge = None
|
||||
|
|
|
|||
Loading…
Reference in New Issue