approximation algorithms for hard capacitated k facility location problems

• DOI: 10.48550/arxiv.1311.4759
• Publication Date: 2015-04-01
• Authors: Pieter L. van den...; Dion Gijswijt; Karen Aardal; Karen Aardal; Shanfei Li; Shanfei Li
• Keywords: FOS: Computer and information sciences; Optimization and Control (math.OC); Computer Science - Data Structures and Algorithms; FOS: Mathematics; 0211 other engineering and technologies; Data Structures and Algorithms (cs.DS); 02 engineering and technology; 90B80 (primary), 68W25 (secondary); Mathematics - Optimization and Control

We study the capacitated $k$-facility location problem, in which we are given a set of clients with demands, a set of facilities with capacities and a constant number $k$. It costs $f_i$ to open facility $i$, and $c_{ij}$ for facility $i$ to serve one unit of demand from client $j$. The objective is to open at most $k$ facilities serving all the demands and satisfying the capacity constraints while minimizing the sum of service and opening costs. In this paper, we give the first fully polynomial time approximation scheme (FPTAS) for the single-sink (single-client) capacitated $k$-facility location problem. Then, we show that the capacitated $k$-facility location problem with uniform capacities is solvable in polynomial time if the number of clients is fixed by reducing it to a collection of transportation problems. Third, we analyze the structure of extreme point solutions, and examine the efficiency of this structure in designing approximation algorithms for capacitated $k$-facility location problems. Finally, we extend our results to obtain an improved approximation algorithm for the capacitated facility location problem with uniform opening cost.<br/>We add new results obtained with Karen Aardal and Pieter van den Berg to the previous version<br/>