Geometric max coverage is approximable strictly better than 1−1/e by combining LP rounding with a greedy warm-up, for every family with linear 2-shallow cell complexity; the paper also gives faster FPT-AS, an EPTAS for continuous fat shapes, and matching hardness.
Approximation Schemes for Geometric Coverage Problems , booktitle =
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Approximation Algorithms for Geometric Maximum Coverage
Geometric max coverage is approximable strictly better than 1−1/e by combining LP rounding with a greedy warm-up, for every family with linear 2-shallow cell complexity; the paper also gives faster FPT-AS, an EPTAS for continuous fat shapes, and matching hardness.