Warning

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')
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: [] 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