A Note on the Random Greedy Independent Set Algorithm

摘要

Let r be a fixed constant and let H be an r-uniform, D-regular hypergraph on N vertices. Assume further that D > N-epsilon for some epsilon > 0. Consider the random greedy algorithm for forming an independent set in H. An independent set is chosen at random by iteratively choosing vertices at random to be in the independent set. At each step we chose a vertex uniformly at random from the collection of vertices that could be added to the independent set (i.e. the collection of vertices v with the property that v is not in the current independent set I and I U {v} contains no edge in H). Note that this process terminates at a maximal subset of vertices with the property that this set contains no edge of H; that is, the process terminates at a maximal independent set.