In this paper, we study uniform hard capacitated facility location problem. The standard LP for the problem is known to have an unbounded integrality gap. We present constant factor approximation by rounding a solution to the standard LP with a slight $(1+\epsilon )$ violation in the capacities.

Our result shows that the standard LP is not too bad.

Our algorithm is simple and more efficient as compared to the strengthened LP-based true approximation that uses the inefficient ellipsoid method with a separation oracle. True approximations are also known for the problem using local search techniques that suffer from the problem of convergence. Moreover, solutions based on standard LP are easier to integrate with other LP-based algorithms.

The result is also extended to give the first approximation for uniform hard capacitated $k$-facility location problem violating the capacities by a factor of $(1+\epsilon )$ and breaking the barrier of 2 in capacity violation. The result violates the cardinality by a factor of $\frac{2}{1+\epsilon }$.

在本文中，我们研究了统一硬电容设施选址问题。已知该问题的标准 LP 具有无限的完整性差距。我们通过将标准 LP 的解四舍五入来呈现常数因子近似值$(1+\epsilon )$违反能力。

我们的结果表明，标准 LP 还不错。

与使用带有分离预言的低效椭圆体方法的基于 LP 的强化真近似相比，我们的算法更简单、更有效。真正的近似也因使用受收敛问题困扰的局部搜索技术的问题而闻名。此外，基于标准 LP 的解决方案更容易与其他基于 LP 的算法集成。

结果也被扩展为给出均匀硬电容的第一个近似值$ķ$- 设施选址问题超出容量的一个因素$(1+\epsilon )$并打破容量违规2的障碍。结果违反了基数的一个因素$\frac{2}{1+\epsilon }$.