Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the lor-bounded facility location problem, which generalizes the classical uncapacitated facility location problem in that it comes with lor bound constraints for the number of clients assigned to a facility in the case that this facility is opened. This problem was introduced independently in the papers by Karger and Minkoff [12] and by Guha, Meyerson, and Munagala [7], both of which give bicriteria approximation algorithms for it. These bicriteria algorithms come within a constant factor of the optimal solution cost, but they also violate the lor bound constraints by a constant factor. Our result in this paper is the first true approximation algorithm for the lor-bounded facility location problem, which respects the lor bound constraints and achieves a constant approximation ratio for the objective function. The main technical idea for the design of the algorithm is a reduction to the capacitated facility location problem, which has known constant-factor approximation algorithms.
['Zoya Svitkina']
I am writing a research paper on a idea Lower-bounded facility location
[{"from": "human", "value": "I am writing a research paper on a idea Lower-bounded facility location"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the lor-bounded facility location problem, which generalizes the classical uncapacitated facility location problem in that it comes with lor bound constraints for the number of clients assigned to a facility in the case that this facility is opened. This problem was introduced independently in the papers by Karger and Minkoff [12] and by Guha, Meyerson, and Munagala [7], both of which give bicriteria approximation algorithms for it. These bicriteria algorithms come within a constant factor of the optimal solution cost, but they also violate the lor bound constraints by a constant factor. Our result in this paper is the first true approximation algorithm for the lor-bounded facility location problem, which respects the lor bound constraints and achieves a constant approximation ratio for the objective function. The main technical idea for the design of the algorithm is a reduction to the capacitated facility location problem, which has known constant-factor approximation algorithms."}]