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Lazy delta updates of T-vertex duals

This commit is contained in:
Joris van Rantwijk 2024-05-26 20:55:54 +02:00
parent 6318de3b1f
commit 7cc1666cf2
1 changed files with 141 additions and 57 deletions
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198
python/mwmatching.py
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@ -443,23 +443,26 @@ class _NonTrivialBlossom(_Blossom):
self.edges: list[tuple[int, int]] = edges
# Every non-trivial blossom has a variable in the dual LPP.
# New blossoms start with dual variable 0.
#
# If this is a top-level S-blossom,
# "dual_var" is the value of the dual variable minus 2 times
# the running sum of delta steps.
# The value of the dual variable changes through delta steps,
# but these changes are implemented as lazy updates.
#
# If this is a top-level T-blossom,
# "dual_var" is the value of the dual variable plus 2 times
# the running sum of delta steps.
# The true dual value of a top-level S-blossom is
# blossom.dual_var + ctx.delta_sum_2x
#
# In all other cases,
# "dual_var" is the current value of the dual variable.
# The true dual value of a top-level T-blossom is
# blossom.dual_var - ctx.delta_sum_2x
#
# The true dual value of any other type of blossom is simply
# blossom.dual_var
#
# Note that "dual_var" is invariant under delta steps.
#
# New blossoms start with dual variable 0.
self.dual_var: float = 0
# Support variable for lazy updating of vertex dual variables.
self.vertex_dual_offset: float = 0
# If this is a top-level T-blossom,
# "delta4_node" is the corresponding node in the delta4 queue.
# Otherwise "delta4_node" is None.
@ -540,23 +543,29 @@ class _MatchingContext:
# Initially all vertices are trivial top-level blossoms.
self.vertex_top_blossom: list[_Blossom] = self.trivial_blossom.copy()
# Initial dual value of all vertices times 2.
# Multiplication by 2 ensures that the values are integers
# if all edge weights are integers.
# All vertex duals are initialized to half the maximum edge weight.
#
# Vertex duals are initialized to half the maximum edge weight.
# "start_vertex_dual_2x" is 2 times the initial vertex dual value.
#
# Pre-multiplication by 2 ensures that the values are integers
# if all edge weights are integers.
self.start_vertex_dual_2x = max(w for (_x, _y, w) in graph.edges)
# Every vertex has a variable in the dual LPP.
#
# For an unlabeled vertex "x",
# "vertex_dual_2x[x]" is 2 times the dual variable of vertex "x".
# The value of the dual variable changes through delta steps,
# but these changes are implemented as lazy updates.
#
# For an S-vertex "x",
# "vertex_dual_2x[x]" is 2 times the dual variable of vertex "x"
# plus two times the running sum of delta steps.
# The true dual value of an S-vertex is
# (vertex_dual_2x[x] - delta_sum_2x) / 2
#
# For a T-vertex "x", ... TODO
# The true dual value of a T-vertex is
# (vertex_dual_2x[x] + delta_sum_2x + B(x).vertex_dual_offset) / 2
#
# The true dual value of an unlabeled vertex is
# (vertex_dual_2x[x] + B(x).vertex_dual_offset) / 2
#
# Note that "vertex_dual_2x" is invariant under delta steps.
self.vertex_dual_2x: list[float]
self.vertex_dual_2x = num_vertex * [self.start_vertex_dual_2x]
@ -606,6 +615,14 @@ class _MatchingContext:
dual_2x -= self.delta_sum_2x
if by.label == _LABEL_S:
dual_2x -= self.delta_sum_2x
if bx.label == _LABEL_T:
dual_2x += self.delta_sum_2x
if by.label == _LABEL_T:
dual_2x += self.delta_sum_2x
if isinstance(bx, _NonTrivialBlossom):
dual_2x += bx.vertex_dual_offset
if isinstance(by, _NonTrivialBlossom):
dual_2x += by.vertex_dual_offset
return dual_2x - 2 * w
#
@ -711,20 +728,18 @@ class _MatchingContext:
def assign_vertex_label_s(self, blossom: _Blossom) -> None:
"""Adjust after assigning label S to previously unlabeled vertices."""
# Prepare for lazy updating of S-vertex dual variables.
vertices = blossom.vertices()
for x in vertices:
self.vertex_dual_2x[x] += self.delta_sum_2x
# Add the new S-vertices to the scan queue.
vertices = blossom.vertices()
self.scan_queue.extend(vertices)
def remove_vertex_label_s(self, blossom: _Blossom) -> None:
"""Adjust after removing labels from S-vertices."""
# Prepare for lazy updating of S-vertex dual variables.
vertex_dual_fixup = self.delta_sum_2x
if isinstance(blossom, _NonTrivialBlossom):
vertex_dual_fixup += blossom.vertex_dual_offset
blossom.vertex_dual_offset = 0
# Catch up with lazy updates to S-vertex dual variables.
for x in blossom.vertices():
self.vertex_dual_2x[x] -= self.delta_sum_2x
for x in vertices:
self.vertex_dual_2x[x] += vertex_dual_fixup
def assign_blossom_label_t(self, blossom: _Blossom) -> None:
"""Assign label T to an unlabeled top-level blossom."""
@ -735,14 +750,22 @@ class _MatchingContext:
if isinstance(blossom, _NonTrivialBlossom):
# Prepare for lazy updates to T-blossom dual variables.
# Prepare for lazy updating of T-blossom dual variables.
blossom.dual_var += self.delta_sum_2x
# Prepare for lazy updating of T-vertex dual variables.
blossom.vertex_dual_offset -= self.delta_sum_2x
# Insert blossom into the delta4 queue.
assert blossom.delta4_node is None
blossom.delta4_node = self.delta4_queue.insert(blossom.dual_var,
blossom)
else:
# Prepare for lazy updating of T-vertex dual variables.
self.vertex_dual_2x[blossom.base_vertex] -= self.delta_sum_2x
def remove_blossom_label_t(self, blossom: _Blossom) -> None:
"""Remove label T from a top-level T-blossom."""
@ -757,9 +780,66 @@ class _MatchingContext:
self.delta4_queue.delete(blossom.delta4_node)
blossom.delta4_node = None
# Catch up with lazy updates to T-blossom dual variable.
# Unwind lazy updates to T-blossom dual variable.
blossom.dual_var -= self.delta_sum_2x
# Unwind lazy updates of T-vertex dual variables.
blossom.vertex_dual_offset += self.delta_sum_2x
else:
# Unwind lazy updates of T-vertex dual variables.
self.vertex_dual_2x[blossom.base_vertex] += self.delta_sum_2x
def reset_blossom_label(self, blossom: _Blossom) -> None:
"""Remove blossom label and calculate true dual variables."""
assert blossom.parent is None
if blossom.label == _LABEL_S:
# Remove label.
blossom.label = _LABEL_NONE
# Unwind lazy delta updates to S-blossom dual variable.
if isinstance(blossom, _NonTrivialBlossom):
blossom.dual_var += self.delta_sum_2x
assert blossom.vertex_dual_offset == 0
# Unwind lazy delta updates to S-vertex dual variables.
vertex_dual_fixup = -self.delta_sum_2x
for x in blossom.vertices():
self.vertex_dual_2x[x] += vertex_dual_fixup
elif blossom.label == _LABEL_T:
# Remove label.
blossom.label = _LABEL_NONE
# Prepare to unwind lazy delta updates to vertices.
vertex_dual_fixup = self.delta_sum_2x
if isinstance(blossom, _NonTrivialBlossom):
# Unwind lazy delta updates to T-blossom dual variable.
blossom.dual_var -= self.delta_sum_2x
# Prepare to unwind lazy delta updates to vertices.
vertex_dual_fixup += blossom.vertex_dual_offset
blossom.vertex_dual_offset = 0
# Unwind lazy delta updates to T-vertex dual variables.
for x in blossom.vertices():
self.vertex_dual_2x[x] += vertex_dual_fixup
else:
# Unwind lazy delta updates to vertex dual variables.
if isinstance(blossom, _NonTrivialBlossom):
vertex_dual_fixup = blossom.vertex_dual_offset
blossom.vertex_dual_offset = 0
for x in blossom.vertices():
self.vertex_dual_2x[x] += vertex_dual_fixup
def reset_stage(self) -> None:
"""Reset data which are only valid during a stage.
@ -769,13 +849,13 @@ class _MatchingContext:
This function takes time O(n).
"""
# Remove blossom labels.
# Remove blossom labels and unwind lazy dual updates.
for blossom in self.trivial_blossom + self.nontrivial_blossom:
if blossom.label == _LABEL_S:
self.remove_blossom_label_s(blossom)
self.remove_vertex_label_s(blossom)
elif blossom.label == _LABEL_T:
self.remove_blossom_label_t(blossom)
if blossom.parent is None:
self.reset_blossom_label(blossom)
if isinstance(blossom, _NonTrivialBlossom):
blossom.delta4_node = None
assert blossom.label == _LABEL_NONE
blossom.tree_edge = None
# Clear the scan queue.
@ -787,7 +867,7 @@ class _MatchingContext:
# Reset delta queues.
self.delta3_queue.clear()
self.delta3_set.clear()
assert self.delta4_queue.empty()
self.delta4_queue.clear()
def trace_alternating_paths(self, x: int, y: int) -> _AlternatingPath:
"""Trace back through the alternating trees from vertices "x" and "y".
@ -968,15 +1048,22 @@ class _MatchingContext:
self.delta4_queue.delete(blossom.delta4_node)
blossom.delta4_node = None
# Prepare to push lazy delta updates down to the sub-blossoms.
vertex_dual_fixup = self.delta_sum_2x + blossom.vertex_dual_offset
blossom.vertex_dual_offset = 0
# Convert sub-blossoms into top-level blossoms.
for sub in blossom.subblossoms:
assert sub.label == _LABEL_NONE
sub.parent = None
if isinstance(sub, _NonTrivialBlossom):
sub.vertex_dual_offset = vertex_dual_fixup
for x in sub.vertices():
self.vertex_top_blossom[x] = sub
else:
self.vertex_top_blossom[sub.base_vertex] = sub
x = sub.base_vertex
self.vertex_dual_2x[x] += vertex_dual_fixup
self.vertex_top_blossom[x] = sub
# The expanding blossom was part of an alternating tree, linked to
# a parent node in the tree via one of its subblossoms, and linked to
@ -1030,16 +1117,24 @@ class _MatchingContext:
assert blossom.parent is None
assert blossom.label == _LABEL_NONE
# Prepare to push lazy delta updates down to the sub-blossoms.
vertex_dual_offset = blossom.vertex_dual_offset
blossom.vertex_dual_offset = 0
# Convert sub-blossoms into top-level blossoms.
for sub in blossom.subblossoms:
assert sub.label == _LABEL_NONE
sub.parent = None
if isinstance(sub, _NonTrivialBlossom):
assert sub.vertex_dual_offset == 0
sub.vertex_dual_offset = vertex_dual_offset
for x in sub.vertices():
self.vertex_top_blossom[x] = sub
else:
self.vertex_top_blossom[sub.base_vertex] = sub
x = sub.base_vertex
self.vertex_dual_2x[x] += vertex_dual_offset
self.vertex_top_blossom[x] = sub
# Delete the expanded blossom.
self.nontrivial_blossom.remove(blossom)
@ -1448,20 +1543,6 @@ class _MatchingContext:
return (delta_type, delta_2x, delta_edge, delta_blossom)
def substage_apply_delta_step(self, delta_2x: float) -> None:
"""Apply a delta step to the dual LPP variables."""
num_vertex = self.graph.num_vertex
self.delta_sum_2x += delta_2x
# Apply delta to dual variables of all vertices.
for x in range(num_vertex):
xlabel = self.vertex_top_blossom[x].label
if xlabel == _LABEL_T:
# T-vertex: add delta to dual variable.
self.vertex_dual_2x[x] += delta_2x
#
# Main stage function:
#
@ -1514,8 +1595,11 @@ class _MatchingContext:
(delta_type, delta_2x, delta_edge, delta_blossom
) = self.substage_calc_dual_delta()
# Apply the delta step to the dual variables.
self.substage_apply_delta_step(delta_2x)
# Update the running sum of delta steps.
# This implicitly updates the dual variables as needed, because
# the running delta sum is taken into account when calculating
# dual values.
self.delta_sum_2x += delta_2x
if delta_type == 2:
# Use the edge from S-vertex to unlabeled vertex that got