Approximations of weighted independent set and hereditary subset problems

The focus of this study is to clarify the approximability of weighted versions of the maximum independent set problem. In particular, we report improved performance ratios in bounded-degree graphs, inductive graphs, and general graphs, as well as for the unweighted problem in sparse graphs. Where possible, the techniques are applied to related hereditary subgraph and subset problem, obtaining ratios better than previously reported for e.g. Weighted Set Packing, Longest Common Subsequence, and Independent Set in hypergraphs.