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This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

Source code for networkx.algorithms.dominance

"""
Dominance algorithms.
"""

__author__ = 'ysitu <ysitu@users.noreply.github.com>'
# Copyright (C) 2014 ysitu <ysitu@users.noreply.github.com>
# All rights reserved.
# BSD license.

from functools import reduce
import networkx as nx
from networkx.utils import not_implemented_for

__all__ = ['immediate_dominators', 'dominance_frontiers']


@not_implemented_for('undirected')
[docs]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
[docs]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: [] for u in idom} for u in idom: if len(G.pred[u]) - int(u in G.pred[u]) >= 2: p = set() for v in G.pred[u]: while v != idom[u] and v not in p: p.add(v) v = idom[v] p.discard(u) for v in p: df[v].append(u) return df