Weighted fractional and integral k-matching in hypergraphs Original Research Article

We consider the problem of finding polynomial-time approximations of maximal weighted k-matchings in a hypergraph and investigate the relationship between the integral and fractional maxima of the corresponding 0–1 integer linear program and its LP-relaxation. We extend results of Raghavan, who gave a deterministic approximation algorithm for unweighted k-matching, to the weighted case and compare the so obtained lower bound for the ratio of the integer and fractional maximum with a lower bound of Aharoni et al. (1985) and Alon et al. (1992).