LP-based approximation for uniform capacitated facility location problem

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2022-08-01 DOI:10.1016/j.disopt.2022.100723

Sapna Grover , Neelima Gupta , Samir Khuller

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引用次数: 1

Abstract

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 $(1 + ϵ)$ 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 $(1 + ϵ)$ and breaking the barrier of 2 in capacity violation. The result violates the cardinality by a factor of $\frac{2}{1 + ϵ}$ .

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均匀容能设施选址问题的lp逼近

本文研究了均匀硬容设施选址问题。已知该问题的标准LP具有无界的完整性间隙。我们通过在容量中有轻微(1+ λ)违反的标准LP的解进行四舍五入，提出常数因子近似。我们的结果表明，标准LP并不差。与使用效率低下的椭球方法和分离预言器的基于强化lp的真近似相比，我们的算法简单有效。真正的近似也因使用局部搜索技术而受到收敛问题的困扰而闻名。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。结果也得到了推广，给出了一致硬容化k-设施定位问题的第一个近似，该问题违反容量的系数为(1+ λ)，并且在容量违反中打破了2的障碍。结果违背了基数性的一个因子(21+ λ)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.