Maximum Clique Branch Bound

Problem

Find a lexicographically smallest maximum clique with a branch-and-bound search.

Maintain a candidate set, branch on the node with the most connections inside it, and prune when the current clique plus candidates cannot beat the best. Return the clique as a sorted list of nodes. edges is a list of [u, v] pairs and n is small.

Hint

Coloring-based bounds make maximum clique tractable far beyond the naive O(2^n).

Test cases

case 1

in: [4,[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]]]

expected: [0,1,2,3]

case 2

in: [5,[[0,1],[1,2],[2,3],[3,4],[4,0]]]

expected: [0,1]

case 3

in: [5,[[0,1],[0,2],[1,2],[2,3],[3,4],[2,4]]]

expected: [0,1,2]

Starter codePython

def maximum_clique_branch_bound(n, edges):
    # Your code here
    pass

3 test cases · run your code against them in the editor