Approximating weighted induced matchings

An induced matching is a matching where no two edges are connected by a third edge. Finding a maximum induced matching on graphs with maximum degree Δ, for Δ≥3, is known to be NP-complete. In this work we consider the weighted version of this problem, which has not been extensively studied in the literature. We devise an almost tight fractional local ratio algorithm with approximation ratio Δ, which proves to be effective also in practice. Furthermore, we show that a simple greedy algorithm applied to K1,k-free graphs yields an approximation ratio 2k−3. We explore the behavior of this algorithm on subclasses of chair-free graphs and we show that it yields an approximation ratio k when restricted to (K1,k,chair)-free graphs.