Approximations of weighted independent set and hereditary subset problems

Abstract

The focus of this study is to clarify the approximability of the important versions of the maximum independent set problem, and to apply, where possible, the technique to related hereditary subgraph and subset problem. We report improved performance ratios for the In- dependent Set problem in weighted general graphs, weighted bounded- degree graphs, and in sparse graphs. Other problems with better than previously reported ratios include Weighted Set Packing, Longest Sub- sequence, Maximum Independent Sequence, and Independent Set in hy- pergraphs.