Approximation algorithms for covering problems

TL;DR: A polynomial-time approximation scheme for k-vertex cover on planar graphs, and for covering points in Rd by disks is obtained, and an approximation of 4/3 is obtained for instances where each set has cardinality at most three.

TL;DR: It is shown that if the weights are homogeneous (i.e., proportional to the potential coverage of the sets) then any minimal cover is a good approximation, and it is sufficient to repeatedly subtract a homogeneous weight function from the given weight function.

TL;DR: We show that if the weights are homogeneous (i.e., proportional to the potential coverage of the sets) then any minimal cover is a good approximation.

TL;DR: In this paper, the authors studied the poc-fvs for graph classes defined by a finite family H of forbidden induced subgraphs, and characterized exactly those finite families H for which the price of connectivity for feedback vertex set for H -free graphs is upper bounded by a constant.