There is an undirected graph G = (V = {v1, . . . , vn}, E). There are a total of n! possible orderings of these vertices. Pick one such ordering uniformly at random σ = (σ1, . . . , σn). Then consider the following process: Begin with S = ∅. Then, at each step (for i = 1 to n), if for all u ∈ S, (u, vσi ) ∈/ E, add vσi to S. Denote by d the maximum degree of a vertex of V . Prove that the proposed algorithm achieves an independent set with expected value of at least 1/d fraction of the optimal solution.

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