LP-Based Algorithms for Capacitated Facility Location

Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of algorithmic methodologies, such as LP-rounding and primal-dual method, have been applied to and evolved from algorithms for this problem. Unfortunately, this collection of powerful algorithmic techniques had not yet been applicable to the more general capacitated facility location problem. In fact, all of the known algorithms with good performance guarantees were based on a single technique, local search, and no linear programming relaxation was known to efficiently approximate the problem. In this paper, we present a linear programming relaxation with constant integrality gap for capacitated facility location. We demonstrate that the fundamental theories of multi-commodity flows and matchings provide key insights that lead to the strong relaxation. Our algorithmic proof of integrality gap is obtained by finally accessing the rich toolbox of LP-based methodologies: we present a constant factor approximation algorithm based on LP-rounding.

Authors

• Hyung-Chan An
• Mohit Singh
• Ola Svensson

Keywords

• Approximation algorithms
• Approximation methods
• Algorithm design and analysis
• Linear programming
• Standards
• Measurement
• Polynomials
• Local Facilities
• Facility Location Problem
• LP-based Algorithm
• Local Search
• Estimation Algorithm
• Constant Factor
• Local Problems
• Combinatorial Problem
• Algorithm For Problem
• Interior Point Method
• Constant Approximation
• Performance Guarantees
• Efficient Approximation
• Linear Relaxation
• Constant Gap
• Linear Programming Relaxation
• Target Value
• Feasible Solution
• First Approximation
• Facilities In Settings
• Fractional Solution
• Integral Solution
• Knapsack Problem
• Steps Of Algorithm
• Capacity Of Facilities
• Operation Of Facilities
• Residual Problems
• Network Flow
• Part Of The Solution
• facility location