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The uncapacitated facility location has always been an important problem dueto its connection to operational research and infrastructure planning. Byrkaobtained an algorithm that is parametrized by $\gamma$ and proved that it isoptimal when $\gamma>1.6774$. He also proved that the algorithm achieved anapproximation ratio of 1.50. A later work by Shi Li achieved an approximationfactor of 1.488. In this research, we studied these algorithms and severalrelated works. Although we didn't improve upon the algorithm of Shi Li, ourwork did provide some insight into the problem. We also reframed the problem asa vector game, which provided a framework to design balanced algorithms forthis problem.

An Attempt to Design a Better Algorithm for the Uncapacitated Facility Location Problem