在Python 2.7中实现Karger Min Cut时出错

Question

I ran into a deadlock when implementing Karger Min Cut algorithm in Python. I broke my head but still can't figure out why my implementation does not work, while it works fine with pencil and paper...

Consider a graph with four nodes 1, 2, 3, 4 and five edges

[1, 2], [1, 3], [2, 3], [2, 4], [3, 4] .

In python, I represented them by two lists:

nodes = [1, 2, 3, 4]
edges = [[1, 2], [1, 3], [2, 3], [2, 4], [3, 4]]

My idea is: randomly choose an edge, say [1, 3] , collapse it, remove node = 3 from nodes list as if 3 is merged into 1 and, remove edge [1, 3] from edges list.

Now the two lists look like:

nodes = [1, 2, 4]
edges = [[1, 2], [2, 3], [2, 4], [3, 4]]

As 3 is merged into 1, the edges list is further updated to

edges = [[1, 2], [2, 1], [2, 4], [1, 4]] 

by changing all 3 in the resulting edges list to 1.

This completes the first loop.

In the second loop, suppose edge [1, 2] is randomly chosen from the edges list, then repeat the above steps I got so that

nodes = [1, 4]
edges = [[2, 1], [2, 4], [1, 4]] 

which is further changed to [[1, 1], [1, 4], [1, 4]] . As [1, 1] indicates a self loop, it is removed and the resulting edges list for this round is [[1, 4], [1, 4]]

As the number of nodes is two, the process ends and the number of min cuts is 2, the length of the final edges list.

So my implementation in Python is as follows:

import numpy as np


nodes = []
edges = []


f = open("kargerMinCut.txt", "r")
# The txt file has the form of an adjacency list
# The link to the txt file is at the very end          

for l in f:
    v = l.split()
    # The first element of each line is a (distinct)
    # vertex and is appended to nodes list.    
    nodes.append(int(v[0]))
    for u in v[1:]:
        # Edges list has the form as described in my 4 nodes example
        # above, which is unlike what in an typical adjacency list for
        # an undirected graph is. Here, if node 1 and node 2 share 
        # an edge, then edge [1, 2] only appears once in the "edges"
        # list, edge [2, 1] is not, which is why I used "set" below.
        edge = [int(v[0])]
        edge.append(int(u))
        count = 0
        for edg in edges:
            if (set(edg) == set(edge)):
                count += 1
        if (count == 0):
            edges.append(edge)

f.close()


while (len(nodes) > 2):
    # Number of current edges
    m = len(edges)
    # Choose a random edge uniformly 
    idx = np.random.randint(m)
    edgeChosen = edges[idx]
    # Two corresponding nodes of the chosen edge
    i = edgeChosen[0]
    j = edgeChosen[1]

    # Remove the second one from nodes list
    nodes.remove(j)
    # Remove the chosen edge from edges list
    del edges[idx]

    # Change all "j"s to "i"
    for ed in edges:
        for e in ed:
            if e == j:
                e = i

    # Remove those [i, i] edges (self loop)
    for ed in edges[:]:
        if len(set(ed)) == 1:
            edges.remove(ed)


print len(edges)

This is just one run of the Karger Min Cut algorithm. Although those for loops in the while loop is inefficient, I just wanna have a try on this idea. I experimented the above code on an input with 200 nodes and 2000+ edges.

But no matter what I did, Python gives the following error after successfully removing a couple of nodes and edges :

nodes.remove(j)
ValueError: list.remove(x): x not in list

which is kind of funny. If x is not in nodes list, it means x is one of the "j"s previously included in a chosen edge and was either removed or changed to the corresponding "i".

However, I cannot find what is wrong with my code. Am I missing something? Any ideas on it? Thanks a lot.

Link to the data file (great thanks to nischayn22 on GitHub): https://github.com/nischayn22/PythonScripts/blob/master/kargerMinCut.txt

Answer 1

Here's a pretty rudimentary working version. This code can be improved in a lot of ways but it works and should point you in the direction of how to do things right.

from random import randint

nodes = [1,2,3,4]
edges = [[1, 2], [1, 3], [2, 3], [2, 4], [3, 4]]


while (len(nodes) > 2):
    target_edge = edges[randint(0, len(edges) - 1)]
    replace_with = target_edge[0]
    num_to_replace = target_edge[1]
    for edge in edges:
        if(edge[0] == num_to_replace):
            edge[0] = replace_with
        if(edge[1] == num_to_replace):
            edge[1] = replace_with
    edges.remove(target_edge)
    nodes.remove(num_to_replace)
    #remove self loops
    for edge in edges:
        if(edge[0] == edge[1]):
            edges.remove(edge)
    print(edges)

print(nodes)
print(edges)

Answer 2

The actual part of the code making the error is

edgeChosen = edges[idx]
i = edgeChosen[0]
j = edgeChosen[1]

j is not in nodes.

If you post your full code we could help more.