joris
/
maximum-weight-matching
1
0
Fork 0
Code Pull Requests Activity

Solve slow maintanance of blossom list

This commit is contained in:
Joris van Rantwijk 2024-06-25 21:01:52 +02:00
parent 61524990d7
commit 1a98624f2b
1 changed files with 34 additions and 52 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

86
python/mwmatching.py
View File

@ -5,6 +5,7 @@ Algorithm for finding a maximum weight matching in general graphs.
from __future__ import annotations
import sys
import itertools
import math
from collections.abc import Sequence
from typing import NamedTuple, Optional
@ -404,7 +405,7 @@ class _Blossom:
self.vertex_dual_offset: float = 0
# "marker" is a temporary variable used to discover common
# ancestors in the blossom tree. It is normally False, except
# ancestors in the alternating tree. It is normally False, except
# when used by "trace_alternating_paths()".
self.marker: bool = False
@ -549,7 +550,7 @@ class _MatchingContext:
# the course of the algorithm.
#
# Initially there are no non-trivial blossoms.
self.nontrivial_blossom: list[_NonTrivialBlossom] = []
self.nontrivial_blossom: set[_NonTrivialBlossom] = set()
# "vertex_set_node[x]" represents the vertex "x" inside the
# union-find datastructure of its top-level blossom.
@ -616,12 +617,8 @@ class _MatchingContext:
def __del__(self) -> None:
"""Delete reference cycles during cleanup of the matching context."""
for blossom in self.trivial_blossom:
blossom.vertex_set.clear()
del blossom.vertex_set
blossom.tree_blossoms = None
for blossom in self.nontrivial_blossom:
for blossom in itertools.chain(self.trivial_blossom,
self.nontrivial_blossom):
blossom.vertex_set.clear()
del blossom.vertex_set
blossom.tree_blossoms = None
@ -774,10 +771,6 @@ class _MatchingContext:
# T-vertices.
self.vertex_sedge_queue[x].clear()
for e in self.graph.adjacent_edges[x]:
# TODO -- Postpone this cleanup step to the scanning of
# S-vertex incident edges.
# It will be more efficient, and also simpler to
# reason about final time complexity.
self.vertex_sedge_node[e] = None
self.vertex_set_node[x].set_prio(math.inf)
@ -925,7 +918,8 @@ class _MatchingContext:
def _check_alternating_tree_consistency(self) -> None:
"""TODO -- remove this function, only for debugging"""
for blossom in self.trivial_blossom + self.nontrivial_blossom:
for blossom in itertools.chain(self.trivial_blossom,
self.nontrivial_blossom):
if (blossom.parent is None) and (blossom.label != _LABEL_NONE):
assert blossom.tree_blossoms is not None
assert blossom in blossom.tree_blossoms
@ -938,38 +932,6 @@ class _MatchingContext:
assert blossom.tree_edge is None
assert blossom.tree_blossoms is None
def reset_stage(self) -> None:
"""Reset data which are only valid during a stage.
Marks all blossoms as unlabeled, applies delayed delta updates,
and resets tracking of least-slack edges.
This function takes time O((n + m) * log(n)).
"""
assert not self.scan_queue
for blossom in self.trivial_blossom + self.nontrivial_blossom:
# Remove blossom label.
if (blossom.parent is None) and (blossom.label != _LABEL_NONE):
self.reset_blossom_label(blossom)
assert blossom.label == _LABEL_NONE
# Remove blossom from alternating tree.
blossom.tree_edge = None
blossom.tree_blossoms = None
# Unwind lazy delta updates to vertex dual variables.
if blossom.vertex_dual_offset != 0:
for x in blossom.vertices():
self.vertex_dual_2x[x] += blossom.vertex_dual_offset
blossom.vertex_dual_offset = 0
assert self.delta2_queue.empty()
assert self.delta3_queue.empty()
assert self.delta4_queue.empty()
def remove_alternating_tree(
self,
tree_blossoms: set[_Blossom]
@ -1123,7 +1085,7 @@ class _MatchingContext:
tree_blossoms.add(blossom)
# Insert into the blossom array.
self.nontrivial_blossom.append(blossom)
self.nontrivial_blossom.add(blossom)
# Link the subblossoms to the their new parent.
for sub in subblossoms:
@ -1251,7 +1213,6 @@ class _MatchingContext:
tree_blossoms.add(sub)
# Delete the expanded blossom.
# TODO -- list manipulation is too slow
self.nontrivial_blossom.remove(blossom)
def expand_unlabeled_blossom(self, blossom: _NonTrivialBlossom) -> None:
@ -1291,7 +1252,6 @@ class _MatchingContext:
sub.delta2_node = self.delta2_queue.insert(prio, sub)
# Delete the expanded blossom.
# TODO -- list manipulation is too slow
self.nontrivial_blossom.remove(blossom)
#
@ -1747,7 +1707,7 @@ class _MatchingContext:
# This loop runs through at most O(n) iterations per stage.
while True:
# self._check_alternating_tree_consistency() # TODO -- remove this
self._check_alternating_tree_consistency() # TODO -- remove this
# Consider the incident edges of newly labeled S-vertices.
self.substage_scan()
@ -1807,10 +1767,32 @@ class _MatchingContext:
Also resets tracking of least-slack edges.
This function takes time O(n * log(n)).
It is called only once, at the end of the algorithm.
It is called once, at the end of the algorithm.
"""
# TODO -- move that function in here
self.reset_stage()
assert not self.scan_queue
for blossom in itertools.chain(self.trivial_blossom,
self.nontrivial_blossom):
# Remove blossom label.
if (blossom.parent is None) and (blossom.label != _LABEL_NONE):
self.reset_blossom_label(blossom)
assert blossom.label == _LABEL_NONE
# Remove blossom from alternating tree.
blossom.tree_edge = None
blossom.tree_blossoms = None
# Unwind lazy delta updates to vertex dual variables.
if blossom.vertex_dual_offset != 0:
for x in blossom.vertices():
self.vertex_dual_2x[x] += blossom.vertex_dual_offset
blossom.vertex_dual_offset = 0
assert self.delta2_queue.empty()
assert self.delta3_queue.empty()
assert self.delta4_queue.empty()
def _verify_blossom_edges(