141 lines
3.5 KiB
Python
141 lines
3.5 KiB
Python
# Copyright (C) 2014-2019 by
|
|
# Aric Hagberg <hagberg@lanl.gov>
|
|
# Dan Schult <dschult@colgate.edu>
|
|
# Pieter Swart <swart@lanl.gov>
|
|
# All rights reserved.
|
|
# BSD license.
|
|
#
|
|
# Authors: ysitu (ysitu@users.noreply.github.com)
|
|
"""
|
|
Dominance algorithms.
|
|
"""
|
|
|
|
from functools import reduce
|
|
import networkx as nx
|
|
from networkx.utils import not_implemented_for
|
|
|
|
__all__ = ['immediate_dominators', 'dominance_frontiers']
|
|
|
|
|
|
@not_implemented_for('undirected')
|
|
def immediate_dominators(G, start):
|
|
"""Returns the immediate dominators of all nodes of a directed graph.
|
|
|
|
Parameters
|
|
----------
|
|
G : a DiGraph or MultiDiGraph
|
|
The graph where dominance is to be computed.
|
|
|
|
start : node
|
|
The start node of dominance computation.
|
|
|
|
Returns
|
|
-------
|
|
idom : dict keyed by nodes
|
|
A dict containing the immediate dominators of each node reachable from
|
|
`start`.
|
|
|
|
Raises
|
|
------
|
|
NetworkXNotImplemented
|
|
If `G` is undirected.
|
|
|
|
NetworkXError
|
|
If `start` is not in `G`.
|
|
|
|
Notes
|
|
-----
|
|
Except for `start`, the immediate dominators are the parents of their
|
|
corresponding nodes in the dominator tree.
|
|
|
|
Examples
|
|
--------
|
|
>>> G = nx.DiGraph([(1, 2), (1, 3), (2, 5), (3, 4), (4, 5)])
|
|
>>> sorted(nx.immediate_dominators(G, 1).items())
|
|
[(1, 1), (2, 1), (3, 1), (4, 3), (5, 1)]
|
|
|
|
References
|
|
----------
|
|
.. [1] K. D. Cooper, T. J. Harvey, and K. Kennedy.
|
|
A simple, fast dominance algorithm.
|
|
Software Practice & Experience, 4:110, 2001.
|
|
"""
|
|
if start not in G:
|
|
raise nx.NetworkXError('start is not in G')
|
|
|
|
idom = {start: start}
|
|
|
|
order = list(nx.dfs_postorder_nodes(G, start))
|
|
dfn = {u: i for i, u in enumerate(order)}
|
|
order.pop()
|
|
order.reverse()
|
|
|
|
def intersect(u, v):
|
|
while u != v:
|
|
while dfn[u] < dfn[v]:
|
|
u = idom[u]
|
|
while dfn[u] > dfn[v]:
|
|
v = idom[v]
|
|
return u
|
|
|
|
changed = True
|
|
while changed:
|
|
changed = False
|
|
for u in order:
|
|
new_idom = reduce(intersect, (v for v in G.pred[u] if v in idom))
|
|
if u not in idom or idom[u] != new_idom:
|
|
idom[u] = new_idom
|
|
changed = True
|
|
|
|
return idom
|
|
|
|
|
|
def dominance_frontiers(G, start):
|
|
"""Returns the dominance frontiers of all nodes of a directed graph.
|
|
|
|
Parameters
|
|
----------
|
|
G : a DiGraph or MultiDiGraph
|
|
The graph where dominance is to be computed.
|
|
|
|
start : node
|
|
The start node of dominance computation.
|
|
|
|
Returns
|
|
-------
|
|
df : dict keyed by nodes
|
|
A dict containing the dominance frontiers of each node reachable from
|
|
`start` as lists.
|
|
|
|
Raises
|
|
------
|
|
NetworkXNotImplemented
|
|
If `G` is undirected.
|
|
|
|
NetworkXError
|
|
If `start` is not in `G`.
|
|
|
|
Examples
|
|
--------
|
|
>>> G = nx.DiGraph([(1, 2), (1, 3), (2, 5), (3, 4), (4, 5)])
|
|
>>> sorted((u, sorted(df)) for u, df in nx.dominance_frontiers(G, 1).items())
|
|
[(1, []), (2, [5]), (3, [5]), (4, [5]), (5, [])]
|
|
|
|
References
|
|
----------
|
|
.. [1] K. D. Cooper, T. J. Harvey, and K. Kennedy.
|
|
A simple, fast dominance algorithm.
|
|
Software Practice & Experience, 4:110, 2001.
|
|
"""
|
|
idom = nx.immediate_dominators(G, start)
|
|
|
|
df = {u: set() for u in idom}
|
|
for u in idom:
|
|
if len(G.pred[u]) >= 2:
|
|
for v in G.pred[u]:
|
|
if v in idom:
|
|
while v != idom[u]:
|
|
df[v].add(u)
|
|
v = idom[v]
|
|
return df
|