Improved LP-based Approximation Algorithms for Facility Location with Hard Capacities
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We present LP-based approximation algorithms for the capacitated facility location problem (CFL), a long-standing problem with intriguing unsettled complexity and literature dated back to the 90s. We present an elegant iterative rounding scheme for the MFN relaxation that yields an approximation guarantee of (10+√(67))/2 ≈ 9.0927, a significant improvement upon the previous LP-based ratio due to An et al in 2014. For CFL with cardinality facility cost (CFL-CFC), we present an LP-based 4-approximation algorithm, which surpasses the long-standing ratio of 5 due to Levi et al that ages up for decades since 2004. Our result considerably deepens the current understanding for the CFL problem and indicates that an LP-based ratio strictly better than 5 in polynomial time for the general problem may still be possible to pursue.
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