A Primal-Dual Approximation Algorithm for the Facility Location Problem with Submodular Penalties

Abstract

We consider the facility location problem with submodular penalties (FLPSP), introduced by Hayrapetyan et al. (Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 933-942, 2005), who presented a 2.50-approximation algorithm that is non-combinatorial because this algorithm has to solve the LP-relaxation of an integer program with exponential number of variables. The only known polynomial algorithm for this exponential LP is via the ellipsoid algorithm as the corresponding separation problem for its dual program can be solved in polynomial time. By exploring the properties of the submodular function, we offer a primal-dual 3-approximation combinatorial algorithm for this problem.

A primal-dual approximation algorithm for stochastic facility location problem with service installation costs

“…On the negative side, one cannot obtain an approximation algorithm with a ratio lower than 1.463 for the FLP unless P = NP [6]. We refer to [1][2][3][4][5]7,8,10,14,15,[20][21][22] for more research on the FLP along with its variants.…”

A per-scenario bound for the two-stage stochastic facility location problem with linear penalty

“…Replacing the linear penalty cost by a general monotonically increasing submodular function, the FLPLP can be generalized into the facility location problem with submodular penalty (FLPSP) (cf. [10][11][12][13][14]). We refer the readers to [15][16][17][18][19][20][21][22] and references therein for more variants of the UFLP.…”

Improved Approximation Algorithms for the Facility Location Problems with Linear/Submodular Penalties

“…Chudak and Nagano [8] gave a faster (2.488 + )-approximation algorithm by solving a convex relaxation rather than an LP relaxation of the FLPSP. Recently, Du et al [10] presented a primal-dual 3-approximation algorithm. Li et al [20] further improved the above ratio to 2.375 by combining the primal-dual scheme with the greedy augmentation technique.…”