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maximum-weight-matching
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Raise MatchingFailed when verify fails

This commit is contained in:
Joris van Rantwijk 2023-02-12 21:18:57 +01:00
parent f1a60febe7
commit be0f5c3881
1 changed files with 40 additions and 11 deletions
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51
python/max_weight_matching.py
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@ -45,6 +45,8 @@ def maximum_weight_matching(
Raises: Raises:
ValueError: If the input does not satisfy the constraints. ValueError: If the input does not satisfy the constraints.
TypeError: If the input contains invalid data types. TypeError: If the input contains invalid data types.
MatchingError: If the matching algorithm fails.
This can only happen if there is a bug in the algorithm.
""" """
# Check that the input meets all constraints. # Check that the input meets all constraints.
@ -171,6 +173,14 @@ def adjust_weights_for_maximum_cardinality_matching(
return [(x, y, w + delta) for (x, y, w) in edges] return [(x, y, w + delta) for (x, y, w) in edges]
class MatchingError(Exception):
"""Raised when verification of the matching fails.
This can only happen if there is a bug in the algorithm.
"""
pass
def _check_input_types(edges: list[tuple[int, int, int|float]]) -> None: def _check_input_types(edges: list[tuple[int, int, int|float]]) -> None:
"""Check that the input consists of valid data types and valid """Check that the input consists of valid data types and valid
numerical ranges. numerical ranges.
@ -1669,7 +1679,7 @@ def _verify_blossom_edges(
dual variable are "full". dual variable are "full".
Raises: Raises:
AssertionError: If a blossom with non-zero dual is not full. MatchingError: If a blossom with non-zero dual is not full.
""" """
num_vertex = ctx.graph.num_vertex num_vertex = ctx.graph.num_vertex
@ -1753,7 +1763,12 @@ def _verify_blossom_edges(
# matched to another vertex in the blossom. # matched to another vertex in the blossom.
if blossom.dual_var > 0: if blossom.dual_var > 0:
blossom_num_matched = path_num_matched[depth] blossom_num_matched = path_num_matched[depth]
assert blossom_num_vertex == 2 * blossom_num_matched + 1 if blossom_num_vertex != 2 * blossom_num_matched + 1:
raise MatchingError(
"Verification failed:"
f" blossom with dual={blossom.dual_var}"
f" nvertex={blossom_num_vertex}"
f" nmatched={blossom_num_matched}")
# Update the number of matched edges in the parent blossom to # Update the number of matched edges in the parent blossom to
# take into account the matched edges in this blossom. # take into account the matched edges in this blossom.
@ -1778,17 +1793,21 @@ def _verify_optimum(ctx: _MatchingContext) -> None:
This function takes time O(n**2). This function takes time O(n**2).
Raises: Raises:
AssertionError: If the solution is not optimal. MatchingError: If the solution is not optimal.
""" """
num_vertex = ctx.graph.num_vertex num_vertex = ctx.graph.num_vertex
num_edge = len(ctx.graph.edges) num_edge = len(ctx.graph.edges)
# Double-check that each matched edge actually exists in the graph. # Check that each matched edge actually exists in the graph.
num_matched_vertex = 0 num_matched_vertex = 0
for x in range(num_vertex): for x in range(num_vertex):
if ctx.vertex_mate[x] != -1: y = ctx.vertex_mate[x]
assert ctx.vertex_mate[ctx.vertex_mate[x]] == x if y != -1:
if ctx.vertex_mate[y] != x:
raise MatchingError(
"Verification failed:"
f" asymmetric match of vertex {x} and {y}")
num_matched_vertex += 1 num_matched_vertex += 1
num_matched_edge = 0 num_matched_edge = 0
@ -1796,12 +1815,17 @@ def _verify_optimum(ctx: _MatchingContext) -> None:
if ctx.vertex_mate[x] == y: if ctx.vertex_mate[x] == y:
num_matched_edge += 1 num_matched_edge += 1
assert num_matched_vertex == 2 * num_matched_edge if num_matched_vertex != 2 * num_matched_edge:
raise MatchingError(
f"Verification failed: {num_matched_vertex} matched vertices"
f" inconsistent with {num_matched_edge} matched edges")
# Check that all dual variables are non-negative. # Check that all dual variables are non-negative.
assert min(ctx.vertex_dual_2x) >= 0 assert min(ctx.vertex_dual_2x) >= 0
for blossom in ctx.nontrivial_blossom: for blossom in ctx.nontrivial_blossom:
assert blossom.dual_var >= 0 if blossom.dual_var < 0:
raise MatchingError("Verification failed:"
f" negative blossom dual {blossom.dual_var}")
# Calculate the slack of each edge. # Calculate the slack of each edge.
# A correction will be needed for edges inside blossoms. # A correction will be needed for edges inside blossoms.
@ -1819,12 +1843,17 @@ def _verify_optimum(ctx: _MatchingContext) -> None:
# We now know the correct slack of each edge. # We now know the correct slack of each edge.
# Check that all edges have non-negative slack. # Check that all edges have non-negative slack.
assert min(edge_slack_2x) >= 0 min_edge_slack = min(edge_slack_2x)
if min_edge_slack < 0:
raise MatchingError(
f"Verification failed: negative edge slack {min_edge_slack/2}")
# Check that all matched edges have zero slack. # Check that all matched edges have zero slack.
for e in range(num_edge): for e in range(num_edge):
(x, y, _w) = ctx.graph.edges[e] (x, y, _w) = ctx.graph.edges[e]
if ctx.vertex_mate[x] == y: if ctx.vertex_mate[x] == y and edge_slack_2x[e] != 0:
assert edge_slack_2x[e] == 0 raise MatchingError(
"Verification failed:"
f" matched edge ({x}, {y}) has slack {edge_slack_2x[e]/2}")
# Optimum solution confirmed. # Optimum solution confirmed.