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author shellac
date Mon, 22 Mar 2021 18:12:50 +0000
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"""Functions for computing the Kernighan–Lin bipartition algorithm."""

import networkx as nx
from itertools import count
from networkx.utils import not_implemented_for, py_random_state, BinaryHeap
from import is_partition

__all__ = ["kernighan_lin_bisection"]

def _kernighan_lin_sweep(edges, side):
    This is a modified form of Kernighan-Lin, which moves single nodes at a
    time, alternating between sides to keep the bisection balanced.  We keep
    two min-heaps of swap costs to make optimal-next-move selection fast.
    costs0, costs1 = costs = BinaryHeap(), BinaryHeap()
    for u, side_u, edges_u in zip(count(), side, edges):
        cost_u = sum(w if side[v] else -w for v, w in edges_u)
        costs[side_u].insert(u, cost_u if side_u else -cost_u)

    def _update_costs(costs_x, x):
        for y, w in edges[x]:
            costs_y = costs[side[y]]
            cost_y = costs_y.get(y)
            if cost_y is not None:
                cost_y += 2 * (-w if costs_x is costs_y else w)
                costs_y.insert(y, cost_y, True)

    i = totcost = 0
    while costs0 and costs1:
        u, cost_u = costs0.pop()
        _update_costs(costs0, u)
        v, cost_v = costs1.pop()
        _update_costs(costs1, v)
        totcost += cost_u + cost_v
        yield totcost, i, (u, v)

def kernighan_lin_bisection(G, partition=None, max_iter=10, weight="weight", seed=None):
    """Partition a graph into two blocks using the Kernighan–Lin

    This algorithm partitions a network into two sets by iteratively
    swapping pairs of nodes to reduce the edge cut between the two sets.  The
    pairs are chosen according to a modified form of Kernighan-Lin, which
    moves node individually, alternating between sides to keep the bisection

    G : graph

    partition : tuple
        Pair of iterables containing an initial partition. If not
        specified, a random balanced partition is used.

    max_iter : int
        Maximum number of times to attempt swaps to find an
        improvemement before giving up.

    weight : key
        Edge data key to use as weight. If None, the weights are all
        set to one.

    seed : integer, random_state, or None (default)
        Indicator of random number generation state.
        See :ref:`Randomness<randomness>`.
        Only used if partition is None

    partition : tuple
        A pair of sets of nodes representing the bipartition.

        If partition is not a valid partition of the nodes of the graph.

    .. [1] Kernighan, B. W.; Lin, Shen (1970).
       "An efficient heuristic procedure for partitioning graphs."
       *Bell Systems Technical Journal* 49: 291--307.
       Oxford University Press 2011.

    n = len(G)
    labels = list(G)
    index = {v: i for i, v in enumerate(labels)}

    if partition is None:
        side = [0] * (n // 2) + [1] * ((n + 1) // 2)
            A, B = partition
        except (TypeError, ValueError) as e:
            raise nx.NetworkXError("partition must be two sets") from e
        if not is_partition(G, (A, B)):
            raise nx.NetworkXError("partition invalid")
        side = [0] * n
        for a in A:
            side[a] = 1

    if G.is_multigraph():
        edges = [
                (index[u], sum(e.get(weight, 1) for e in d.values()))
                for u, d in G[v].items()
            for v in labels
        edges = [
            [(index[u], e.get(weight, 1)) for u, e in G[v].items()] for v in labels

    for i in range(max_iter):
        costs = list(_kernighan_lin_sweep(edges, side))
        min_cost, min_i, _ = min(costs)
        if min_cost >= 0:

        for _, _, (u, v) in costs[: min_i + 1]:
            side[u] = 1
            side[v] = 0

    A = {u for u, s in zip(labels, side) if s == 0}
    B = {u for u, s in zip(labels, side) if s == 1}
    return A, B