Independent Sets in Bounded-Degree Hypergraphs

In this paper we analyze several approaches to the Maximum Independent Set problem in hypergraphs with degree bounded by Δ. We propose a general technique that reduces the worst case analysis of certain algorithms to their performance in the case of ordinary graphs. This technique allows us to show that the greedy algorithm that corresponds to the classical greedy set cover algorithm has a performance ratio of (Δ + 1)/2. It also allows us to apply results on local search algorithms of graphs to obtain a (Δ + 1)/2 approximation for a weighted case and (Δ + 3)/5 − ε approximation for an unweighted case. We improve the bound in the weighted case to ⌈(Δ + 1)/3 ⌉ using a simple partitioning algorithm. Finally, we show that another natural greedy algorihthm, that adds vertices of minimum degree, achieves only a ratio of Δ− 1, significantly worse than on ordinary graphs.