The Uncapacitated Facility Location (UFL) problem: given potential facility sites with opening costs and clients with connection costs, open a subset of facilities to minimize total opening + assignment cost. UFL is NP-hard but has a celebrated 1.488-approximation (Li 2013, improving Jain-Mahdian-Saberi 2002 and Byrka-Aardal 2010). LP relaxation gives a lower bound, and the integrality gap is exactly 1.463... (Guha-Khuller 1999). Applications: hospital placement, cloud data center optimization, and k-median clustering.