Python networkx.immediate_dominators() Examples

def _refine_loop(self, graph, head, initial_loop_nodes, initial_exit_nodes):
        refined_loop_nodes = initial_loop_nodes.copy()
        refined_exit_nodes = initial_exit_nodes.copy()

        idom = networkx.immediate_dominators(graph, self._start_node)

        new_exit_nodes = refined_exit_nodes
        while len(refined_exit_nodes) > 1 and new_exit_nodes:
            new_exit_nodes = set()
            for n in list(refined_exit_nodes):
                if all(pred in refined_loop_nodes for pred in graph.predecessors(n)) and dominates(idom, head, n):
                    refined_loop_nodes.add(n)
                    refined_exit_nodes.remove(n)
                    for u in (set(graph.successors(n)) - refined_loop_nodes):
                        new_exit_nodes.add(u)
            refined_exit_nodes |= new_exit_nodes

        refined_loop_nodes = refined_loop_nodes - refined_exit_nodes

        return refined_loop_nodes, refined_exit_nodes 

def test_boost_example(self):
        # Graph taken from Figure 1 of
        # http://www.boost.org/doc/libs/1_56_0/libs/graph/doc/lengauer_tarjan_dominator.htm
        edges = [(0, 1), (1, 2), (1, 3), (2, 7), (3, 4), (4, 5), (4, 6),
                 (5, 7), (6, 4)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 0),
                     {0: 0, 1: 0, 2: 1, 3: 1, 4: 3, 5: 4, 6: 4, 7: 1})
        # Test postdominance.
        with nx.utils.reversed(G):
            assert_equal(nx.immediate_dominators(G, 7),
                         {0: 1, 1: 7, 2: 7, 3: 4, 4: 5, 5: 7, 6: 4, 7: 7}) 

def _post_dominate(reversed_graph, n1, n2):
        """
        Checks whether `n1` post-dominates `n2` in the *original* (not reversed) graph.

        :param networkx.DiGraph reversed_graph:  The reversed networkx.DiGraph instance.
        :param networkx.Node n1:                 Node 1.
        :param networkx.Node n2:                 Node 2.
        :returns bool:                           True/False.
        """

        ds = networkx.immediate_dominators(reversed_graph, n1)
        return n2 in ds 

def test_domrel_png(self):
        # Graph taken from https://commons.wikipedia.org/wiki/File:Domrel.png
        edges = [(1, 2), (2, 3), (2, 4), (2, 6), (3, 5), (4, 5), (5, 2)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 1),
                     {1: 1, 2: 1, 3: 2, 4: 2, 5: 2, 6: 2})
        # Test postdominance.
        with nx.utils.reversed(G):
            assert_equal(nx.immediate_dominators(G, 6),
                         {1: 2, 2: 6, 3: 5, 4: 5, 5: 2, 6: 6}) 

def test_irreducible2(self):
        # Graph taken from Figure 4 of
        # K. D. Cooper, T. J. Harvey, and K. Kennedy.
        # A simple, fast dominance algorithm.
        # Software Practice & Experience, 4:110, 2001.
        edges = [(1, 2), (2, 1), (2, 3), (3, 2), (4, 2), (4, 3), (5, 1),
                 (6, 4), (6, 5)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 6),
                     {i: 6 for i in range(1, 7)}) 

def test_irreducible1(self):
        # Graph taken from Figure 2 of
        # K. D. Cooper, T. J. Harvey, and K. Kennedy.
        # A simple, fast dominance algorithm.
        # Software Practice & Experience, 4:110, 2001.
        edges = [(1, 2), (2, 1), (3, 2), (4, 1), (5, 3), (5, 4)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 5),
                     {i: 5 for i in range(1, 6)}) 

def test_cycle(self):
        n = 5
        G = nx.cycle_graph(n, create_using=nx.DiGraph())
        assert_equal(nx.immediate_dominators(G, 0),
                     {i: max(i - 1, 0) for i in range(n)}) 

def test_path(self):
        n = 5
        G = nx.path_graph(n, create_using=nx.DiGraph())
        assert_equal(nx.immediate_dominators(G, 0),
                     {i: max(i - 1, 0) for i in range(n)}) 

def test_singleton(self):
        G = nx.DiGraph()
        G.add_node(0)
        assert_equal(nx.immediate_dominators(G, 0), {0: 0})
        G.add_edge(0, 0)
        assert_equal(nx.immediate_dominators(G, 0), {0: 0}) 

def test_exceptions(self):
        G = nx.Graph()
        G.add_node(0)
        assert_raises(nx.NetworkXNotImplemented, nx.immediate_dominators, G, 0)
        G = nx.MultiGraph(G)
        assert_raises(nx.NetworkXNotImplemented, nx.immediate_dominators, G, 0)
        G = nx.DiGraph([[0, 0]])
        assert_raises(nx.NetworkXError, nx.immediate_dominators, G, 1) 

def test_boost_example(self):
        # Graph taken from Figure 1 of
        # http://www.boost.org/doc/libs/1_56_0/libs/graph/doc/lengauer_tarjan_dominator.htm
        edges = [(0, 1), (1, 2), (1, 3), (2, 7), (3, 4), (4, 5), (4, 6),
                 (5, 7), (6, 4)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 0),
                     {0: 0, 1: 0, 2: 1, 3: 1, 4: 3, 5: 4, 6: 4, 7: 1})
        # Test postdominance.
        with nx.utils.reversed(G):
            assert_equal(nx.immediate_dominators(G, 7),
                         {0: 1, 1: 7, 2: 7, 3: 4, 4: 5, 5: 7, 6: 4, 7: 7}) 

def test_domrel_png(self):
        # Graph taken from https://commons.wikipedia.org/wiki/File:Domrel.png
        edges = [(1, 2), (2, 3), (2, 4), (2, 6), (3, 5), (4, 5), (5, 2)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 1),
                     {1: 1, 2: 1, 3: 2, 4: 2, 5: 2, 6: 2})
        # Test postdominance.
        with nx.utils.reversed(G):
            assert_equal(nx.immediate_dominators(G, 6),
                         {1: 2, 2: 6, 3: 5, 4: 5, 5: 2, 6: 6}) 

def test_irreducible2(self):
        # Graph taken from Figure 4 of
        # K. D. Cooper, T. J. Harvey, and K. Kennedy.
        # A simple, fast dominance algorithm.
        # Software Practice & Experience, 4:110, 2001.
        edges = [(1, 2), (2, 1), (2, 3), (3, 2), (4, 2), (4, 3), (5, 1),
                 (6, 4), (6, 5)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 6),
                     {i: 6 for i in range(1, 7)}) 

def test_irreducible1(self):
        # Graph taken from Figure 2 of
        # K. D. Cooper, T. J. Harvey, and K. Kennedy.
        # A simple, fast dominance algorithm.
        # Software Practice & Experience, 4:110, 2001.
        edges = [(1, 2), (2, 1), (3, 2), (4, 1), (5, 3), (5, 4)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 5),
                     {i: 5 for i in range(1, 6)}) 

def test_cycle(self):
        n = 5
        G = nx.cycle_graph(n, create_using=nx.DiGraph())
        assert_equal(nx.immediate_dominators(G, 0),
                     {i: max(i - 1, 0) for i in range(n)}) 

def test_path(self):
        n = 5
        G = nx.path_graph(n, create_using=nx.DiGraph())
        assert_equal(nx.immediate_dominators(G, 0),
                     {i: max(i - 1, 0) for i in range(n)}) 

def test_singleton(self):
        G = nx.DiGraph()
        G.add_node(0)
        assert_equal(nx.immediate_dominators(G, 0), {0: 0})
        G.add_edge(0, 0)
        assert_equal(nx.immediate_dominators(G, 0), {0: 0}) 

def test_exceptions(self):
        G = nx.Graph()
        G.add_node(0)
        assert_raises(nx.NetworkXNotImplemented, nx.immediate_dominators, G, 0)
        G = nx.MultiGraph(G)
        assert_raises(nx.NetworkXNotImplemented, nx.immediate_dominators, G, 0)
        G = nx.DiGraph([[0, 0]])
        assert_raises(nx.NetworkXError, nx.immediate_dominators, G, 1) 

def test_boost_example(self):
        # Graph taken from Figure 1 of
        # http://www.boost.org/doc/libs/1_56_0/libs/graph/doc/lengauer_tarjan_dominator.htm
        edges = [(0, 1), (1, 2), (1, 3), (2, 7), (3, 4), (4, 5), (4, 6),
                 (5, 7), (6, 4)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 0),
                     {0: 0, 1: 0, 2: 1, 3: 1, 4: 3, 5: 4, 6: 4, 7: 1})
        # Test postdominance.
        with nx.utils.reversed(G):
            assert_equal(nx.immediate_dominators(G, 7),
                         {0: 1, 1: 7, 2: 7, 3: 4, 4: 5, 5: 7, 6: 4, 7: 7}) 

def test_domrel_png(self):
        # Graph taken from https://commons.wikipedia.org/wiki/File:Domrel.png
        edges = [(1, 2), (2, 3), (2, 4), (2, 6), (3, 5), (4, 5), (5, 2)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 1),
                     {1: 1, 2: 1, 3: 2, 4: 2, 5: 2, 6: 2})
        # Test postdominance.
        with nx.utils.reversed(G):
            assert_equal(nx.immediate_dominators(G, 6),
                         {1: 2, 2: 6, 3: 5, 4: 5, 5: 2, 6: 6}) 

def test_irreducible2(self):
        # Graph taken from Figure 4 of
        # K. D. Cooper, T. J. Harvey, and K. Kennedy.
        # A simple, fast dominance algorithm.
        # Software Practice & Experience, 4:110, 2001.
        edges = [(1, 2), (2, 1), (2, 3), (3, 2), (4, 2), (4, 3), (5, 1),
                 (6, 4), (6, 5)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 6),
                     {i: 6 for i in range(1, 7)}) 

def test_irreducible1(self):
        # Graph taken from Figure 2 of
        # K. D. Cooper, T. J. Harvey, and K. Kennedy.
        # A simple, fast dominance algorithm.
        # Software Practice & Experience, 4:110, 2001.
        edges = [(1, 2), (2, 1), (3, 2), (4, 1), (5, 3), (5, 4)]
        G = nx.DiGraph(edges)
        assert_equal(nx.immediate_dominators(G, 5),
                     {i: 5 for i in range(1, 6)}) 

def test_cycle(self):
        n = 5
        G = nx.cycle_graph(n, create_using=nx.DiGraph())
        assert_equal(nx.immediate_dominators(G, 0),
                     {i: max(i - 1, 0) for i in range(n)}) 

def test_path(self):
        n = 5
        G = nx.path_graph(n, create_using=nx.DiGraph())
        assert_equal(nx.immediate_dominators(G, 0),
                     {i: max(i - 1, 0) for i in range(n)}) 

def test_singleton(self):
        G = nx.DiGraph()
        G.add_node(0)
        assert_equal(nx.immediate_dominators(G, 0), {0: 0})
        G.add_edge(0, 0)
        assert_equal(nx.immediate_dominators(G, 0), {0: 0}) 

def test_exceptions(self):
        G = nx.Graph()
        G.add_node(0)
        assert_raises(nx.NetworkXNotImplemented, nx.immediate_dominators, G, 0)
        G = nx.MultiGraph(G)
        assert_raises(nx.NetworkXNotImplemented, nx.immediate_dominators, G, 0)
        G = nx.DiGraph([[0, 0]])
        assert_raises(nx.NetworkXError, nx.immediate_dominators, G, 1) 

def dominator_forest(self):
        if self._dominator_forest is not None:
            return self._dominator_forest
        self._dominator_forest = DAG()
        for root in self.roots:
            for node, dominated_by in nx.immediate_dominators(self, root).items():
                if node != dominated_by:
                    self._dominator_forest.add_edge(dominated_by, node)
        return self._dominator_forest 

def _compute_dominators(self):
        import networkx
        g = networkx.DiGraph()
        for bb in self.bbs:
            for succ in bb.succ:
                g.add_edge(bb.start, succ.start)
        self._dominators = {self._bb_at[k]: self._bb_at[v] for k, v in networkx.immediate_dominators(g, 0).items()} 

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 

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