path: root/networkx/algorithms/connectivity/tests/test_edge_augmentation.py

import random
import networkx as nx
import itertools as it
from networkx.utils import pairwise
import pytest
from networkx.algorithms.connectivity import k_edge_augmentation
from networkx.algorithms.connectivity.edge_augmentation import (
    collapse,
    complement_edges,
    is_locally_k_edge_connected,
    is_k_edge_connected,
    _unpack_available_edges,
)

# This should be set to the largest k for which an efficient algorithm is
# explicitly defined.
MAX_EFFICIENT_K = 2


def tarjan_bridge_graph():
    # graph from tarjan paper
    # RE Tarjan - "A note on finding the bridges of a graph"
    # Information Processing Letters, 1974 - Elsevier
    # doi:10.1016/0020-0190(74)90003-9.
    # define 2-connected components and bridges
    ccs = [
        (1, 2, 4, 3, 1, 4),
        (5, 6, 7, 5),
        (8, 9, 10, 8),
        (17, 18, 16, 15, 17),
        (11, 12, 14, 13, 11, 14),
    ]
    bridges = [(4, 8), (3, 5), (3, 17)]
    G = nx.Graph(it.chain(*(pairwise(path) for path in ccs + bridges)))
    return G


def test_weight_key():
    G = nx.Graph()
    G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8, 9])
    G.add_edges_from([(3, 8), (1, 2), (2, 3)])
    impossible = {(3, 6), (3, 9)}
    rng = random.Random(0)
    avail_uv = list(set(complement_edges(G)) - impossible)
    avail = [(u, v, {"cost": rng.random()}) for u, v in avail_uv]

    _augment_and_check(G, k=1)
    _augment_and_check(G, k=1, avail=avail_uv)
    _augment_and_check(G, k=1, avail=avail, weight="cost")

    _check_augmentations(G, avail, weight="cost")


def test_is_locally_k_edge_connected_exceptions():
    pytest.raises(nx.NetworkXNotImplemented, is_k_edge_connected, nx.DiGraph(), k=0)
    pytest.raises(nx.NetworkXNotImplemented, is_k_edge_connected, nx.MultiGraph(), k=0)
    pytest.raises(ValueError, is_k_edge_connected, nx.Graph(), k=0)


def test_is_k_edge_connected():
    G = nx.barbell_graph(10, 0)
    assert is_k_edge_connected(G, k=1)
    assert not is_k_edge_connected(G, k=2)

    G = nx.Graph()
    G.add_nodes_from([5, 15])
    assert not is_k_edge_connected(G, k=1)
    assert not is_k_edge_connected(G, k=2)

    G = nx.complete_graph(5)
    assert is_k_edge_connected(G, k=1)
    assert is_k_edge_connected(G, k=2)
    assert is_k_edge_connected(G, k=3)
    assert is_k_edge_connected(G, k=4)


def test_is_k_edge_connected_exceptions():
    pytest.raises(
        nx.NetworkXNotImplemented, is_locally_k_edge_connected, nx.DiGraph(), 1, 2, k=0
    )
    pytest.raises(
        nx.NetworkXNotImplemented,
        is_locally_k_edge_connected,
        nx.MultiGraph(),
        1,
        2,
        k=0,
    )
    pytest.raises(ValueError, is_locally_k_edge_connected, nx.Graph(), 1, 2, k=0)


def test_is_locally_k_edge_connected():
    G = nx.barbell_graph(10, 0)
    assert is_locally_k_edge_connected(G, 5, 15, k=1)
    assert not is_locally_k_edge_connected(G, 5, 15, k=2)

    G = nx.Graph()
    G.add_nodes_from([5, 15])
    assert not is_locally_k_edge_connected(G, 5, 15, k=2)


def test_null_graph():
    G = nx.Graph()
    _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2)


def test_cliques():
    for n in range(1, 10):
        G = nx.complete_graph(n)
        _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2)


def test_clique_and_node():
    for n in range(1, 10):
        G = nx.complete_graph(n)
        G.add_node(n + 1)
        _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2)


def test_point_graph():
    G = nx.Graph()
    G.add_node(1)
    _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2)


def test_edgeless_graph():
    G = nx.Graph()
    G.add_nodes_from([1, 2, 3, 4])
    _check_augmentations(G)


def test_invalid_k():
    G = nx.Graph()
    pytest.raises(ValueError, list, k_edge_augmentation(G, k=-1))
    pytest.raises(ValueError, list, k_edge_augmentation(G, k=0))


def test_unfeasible():
    G = tarjan_bridge_graph()
    pytest.raises(nx.NetworkXUnfeasible, list, k_edge_augmentation(G, k=1, avail=[]))

    pytest.raises(nx.NetworkXUnfeasible, list, k_edge_augmentation(G, k=2, avail=[]))

    pytest.raises(
        nx.NetworkXUnfeasible, list, k_edge_augmentation(G, k=2, avail=[(7, 9)])
    )

    # partial solutions should not error if real solutions are infeasible
    aug_edges = list(k_edge_augmentation(G, k=2, avail=[(7, 9)], partial=True))
    assert aug_edges == [(7, 9)]

    _check_augmentations(G, avail=[], max_k=MAX_EFFICIENT_K + 2)

    _check_augmentations(G, avail=[(7, 9)], max_k=MAX_EFFICIENT_K + 2)


def test_tarjan():
    G = tarjan_bridge_graph()

    aug_edges = set(_augment_and_check(G, k=2)[0])
    print(f"aug_edges = {aug_edges!r}")
    # can't assert edge exactly equality due to non-determinant edge order
    # but we do know the size of the solution must be 3
    assert len(aug_edges) == 3

    avail = [
        (9, 7),
        (8, 5),
        (2, 10),
        (6, 13),
        (11, 18),
        (1, 17),
        (2, 3),
        (16, 17),
        (18, 14),
        (15, 14),
    ]
    aug_edges = set(_augment_and_check(G, avail=avail, k=2)[0])

    # Can't assert exact length since approximation depends on the order of a
    # dict traversal.
    assert len(aug_edges) <= 3 * 2

    _check_augmentations(G, avail)


def test_configuration():
    # seeds = [2718183590, 2470619828, 1694705158, 3001036531, 2401251497]
    seeds = [1001, 1002, 1003, 1004]
    for seed in seeds:
        deg_seq = nx.random_powerlaw_tree_sequence(20, seed=seed, tries=5000)
        G = nx.Graph(nx.configuration_model(deg_seq, seed=seed))
        G.remove_edges_from(nx.selfloop_edges(G))
        _check_augmentations(G)


def test_shell():
    # seeds = [2057382236, 3331169846, 1840105863, 476020778, 2247498425]
    seeds = [18]
    for seed in seeds:
        constructor = [(12, 70, 0.8), (15, 40, 0.6)]
        G = nx.random_shell_graph(constructor, seed=seed)
        _check_augmentations(G)


def test_karate():
    G = nx.karate_club_graph()
    _check_augmentations(G)


def test_star():
    G = nx.star_graph(3)
    _check_augmentations(G)

    G = nx.star_graph(5)
    _check_augmentations(G)

    G = nx.star_graph(10)
    _check_augmentations(G)


def test_barbell():
    G = nx.barbell_graph(5, 0)
    _check_augmentations(G)

    G = nx.barbell_graph(5, 2)
    _check_augmentations(G)

    G = nx.barbell_graph(5, 3)
    _check_augmentations(G)

    G = nx.barbell_graph(5, 4)
    _check_augmentations(G)


def test_bridge():
    G = nx.Graph([(2393, 2257), (2393, 2685), (2685, 2257), (1758, 2257)])
    _check_augmentations(G)


def test_gnp_augmentation():
    rng = random.Random(0)
    G = nx.gnp_random_graph(30, 0.005, seed=0)
    # Randomly make edges available
    avail = {
        (u, v): 1 + rng.random() for u, v in complement_edges(G) if rng.random() < 0.25
    }
    _check_augmentations(G, avail)


def _assert_solution_properties(G, aug_edges, avail_dict=None):
    """Checks that aug_edges are consistently formatted"""
    if avail_dict is not None:
        assert all(
            e in avail_dict for e in aug_edges
        ), "when avail is specified aug-edges should be in avail"

    unique_aug = set(map(tuple, map(sorted, aug_edges)))
    unique_aug = list(map(tuple, map(sorted, aug_edges)))
    assert len(aug_edges) == len(unique_aug), "edges should be unique"

    assert not any(u == v for u, v in unique_aug), "should be no self-edges"

    assert not any(
        G.has_edge(u, v) for u, v in unique_aug
    ), "aug edges and G.edges should be disjoint"


def _augment_and_check(
    G, k, avail=None, weight=None, verbose=False, orig_k=None, max_aug_k=None
):
    """
    Does one specific augmentation and checks for properties of the result
    """
    if orig_k is None:
        try:
            orig_k = nx.edge_connectivity(G)
        except nx.NetworkXPointlessConcept:
            orig_k = 0
    info = {}
    try:
        if avail is not None:
            # ensure avail is in dict form
            avail_dict = dict(zip(*_unpack_available_edges(avail, weight=weight)))
        else:
            avail_dict = None
        try:
            # Find the augmentation if possible
            generator = nx.k_edge_augmentation(G, k=k, weight=weight, avail=avail)
            assert not isinstance(generator, list), "should always return an iter"
            aug_edges = []
            for edge in generator:
                aug_edges.append(edge)
        except nx.NetworkXUnfeasible:
            infeasible = True
            info["infeasible"] = True
            assert len(aug_edges) == 0, "should not generate anything if unfeasible"

            if avail is None:
                n_nodes = G.number_of_nodes()
                assert n_nodes <= k, (
                    "unconstrained cases are only unfeasible if |V| <= k. "
                    f"Got |V|={n_nodes} and k={k}"
                )
            else:
                if max_aug_k is None:
                    G_aug_all = G.copy()
                    G_aug_all.add_edges_from(avail_dict.keys())
                    try:
                        max_aug_k = nx.edge_connectivity(G_aug_all)
                    except nx.NetworkXPointlessConcept:
                        max_aug_k = 0

                assert max_aug_k < k, (
                    "avail should only be unfeasible if using all edges "
                    "does not achieve k-edge-connectivity"
                )

            # Test for a partial solution
            partial_edges = list(
                nx.k_edge_augmentation(G, k=k, weight=weight, partial=True, avail=avail)
            )

            info["n_partial_edges"] = len(partial_edges)

            if avail_dict is None:
                assert set(partial_edges) == set(
                    complement_edges(G)
                ), "unweighted partial solutions should be the complement"
            elif len(avail_dict) > 0:
                H = G.copy()

                # Find the partial / full augmented connectivity
                H.add_edges_from(partial_edges)
                partial_conn = nx.edge_connectivity(H)

                H.add_edges_from(set(avail_dict.keys()))
                full_conn = nx.edge_connectivity(H)

                # Full connectivity should be no better than our partial
                # solution.
                assert (
                    partial_conn == full_conn
                ), "adding more edges should not increase k-conn"

            # Find the new edge-connectivity after adding the augmenting edges
            aug_edges = partial_edges
        else:
            infeasible = False

        # Find the weight of the augmentation
        num_edges = len(aug_edges)
        if avail is not None:
            total_weight = sum(avail_dict[e] for e in aug_edges)
        else:
            total_weight = num_edges

        info["total_weight"] = total_weight
        info["num_edges"] = num_edges

        # Find the new edge-connectivity after adding the augmenting edges
        G_aug = G.copy()
        G_aug.add_edges_from(aug_edges)
        try:
            aug_k = nx.edge_connectivity(G_aug)
        except nx.NetworkXPointlessConcept:
            aug_k = 0
        info["aug_k"] = aug_k

        # Do checks
        if not infeasible and orig_k < k:
            assert info["aug_k"] >= k, f"connectivity should increase to k={k} or more"

        assert info["aug_k"] >= orig_k, "augmenting should never reduce connectivity"

        _assert_solution_properties(G, aug_edges, avail_dict)

    except Exception:
        info["failed"] = True
        print(f"edges = {list(G.edges())}")
        print(f"nodes = {list(G.nodes())}")
        print(f"aug_edges = {list(aug_edges)}")
        print(f"info  = {info}")
        raise
    else:
        if verbose:
            print(f"info  = {info}")

    if infeasible:
        aug_edges = None
    return aug_edges, info


def _check_augmentations(G, avail=None, max_k=None, weight=None, verbose=False):
    """Helper to check weighted/unweighted cases with multiple values of k"""
    # Using all available edges, find the maximum edge-connectivity
    try:
        orig_k = nx.edge_connectivity(G)
    except nx.NetworkXPointlessConcept:
        orig_k = 0

    if avail is not None:
        all_aug_edges = _unpack_available_edges(avail, weight=weight)[0]
        G_aug_all = G.copy()
        G_aug_all.add_edges_from(all_aug_edges)
        try:
            max_aug_k = nx.edge_connectivity(G_aug_all)
        except nx.NetworkXPointlessConcept:
            max_aug_k = 0
    else:
        max_aug_k = G.number_of_nodes() - 1

    if max_k is None:
        max_k = min(4, max_aug_k)

    avail_uniform = {e: 1 for e in complement_edges(G)}

    if verbose:
        print("\n=== CHECK_AUGMENTATION ===")
        print(f"G.number_of_nodes = {G.number_of_nodes()!r}")
        print(f"G.number_of_edges = {G.number_of_edges()!r}")
        print(f"max_k = {max_k!r}")
        print(f"max_aug_k = {max_aug_k!r}")
        print(f"orig_k = {orig_k!r}")

    # check augmentation for multiple values of k
    for k in range(1, max_k + 1):
        if verbose:
            print("---------------")
            print(f"Checking k = {k}")

        # Check the unweighted version
        if verbose:
            print("unweighted case")
        aug_edges1, info1 = _augment_and_check(G, k=k, verbose=verbose, orig_k=orig_k)

        # Check that the weighted version with all available edges and uniform
        # weights gives a similar solution to the unweighted case.
        if verbose:
            print("weighted uniform case")
        aug_edges2, info2 = _augment_and_check(
            G,
            k=k,
            avail=avail_uniform,
            verbose=verbose,
            orig_k=orig_k,
            max_aug_k=G.number_of_nodes() - 1,
        )

        # Check the weighted version
        if avail is not None:
            if verbose:
                print("weighted case")
            aug_edges3, info3 = _augment_and_check(
                G,
                k=k,
                avail=avail,
                weight=weight,
                verbose=verbose,
                max_aug_k=max_aug_k,
                orig_k=orig_k,
            )

        if aug_edges1 is not None:
            # Check approximation ratios
            if k == 1:
                # when k=1, both solutions should be optimal
                assert info2["total_weight"] == info1["total_weight"]
            if k == 2:
                # when k=2, the weighted version is an approximation
                if orig_k == 0:
                    # the approximation ratio is 3 if G is not connected
                    assert info2["total_weight"] <= info1["total_weight"] * 3
                else:
                    # the approximation ratio is 2 if G is was connected
                    assert info2["total_weight"] <= info1["total_weight"] * 2
                _check_unconstrained_bridge_property(G, info1)


def _check_unconstrained_bridge_property(G, info1):
    # Check Theorem 5 from Eswaran and Tarjan. (1975) Augmentation problems
    import math

    bridge_ccs = list(nx.connectivity.bridge_components(G))
    # condense G into an forest C
    C = collapse(G, bridge_ccs)

    p = len([n for n, d in C.degree() if d == 1])  # leafs
    q = len([n for n, d in C.degree() if d == 0])  # isolated
    if p + q > 1:
        size_target = math.ceil(p / 2) + q
        size_aug = info1["num_edges"]
        assert (
            size_aug == size_target
        ), "augmentation size is different from what theory predicts"