摘要：In this announcement, we show that the classical Maximum Coverage problem (MC) admits a PTAS via local search in essentially all cases where the corresponding instances of Set Cover (SC) admit a PTAS via the local search approach by Mustafa and Ray [Nabil H. Mustafa and Saurabh Ray, 2010]. As a corollary, we answer an open question by Badanidiyuru, Kleinberg, and Lee [Ashwinkumar Badanidiyuru et al., 2012] regarding half-spaces in R^3 thereby settling the existence of PTASs for essentially all natural cases of geometric MC problems. As an intermediate result, we show a color-balanced version of the classical planar subdivision theorem by Frederickson [Greg N. Frederickson, 1987]. We believe that some of our ideas may be useful for analyzing local search in other settings involving a hard cardinality constraint.
关键词：balanced separators; maximum coverage; local search; approximation scheme; geometric approximation algorithms
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