The vectors p1, . . . , pN , each in R2 represent the locations of N objects. There are two types of objects: factories and warehouses. The first K objects are factories, whose locations are fixed and given. Our goal in the placement problem to choose the locations of the last N K objects; i.e., the warehouses. Our choice of the locations is guided by an undirected graph; an edge between two objects means we would like them to be close to each other. In least squares placement, we choose the locations pK 1, . . . , pN of warehouses so as to minimize the sum of the squares of the distances between objects connected by an edge, where the L edges of the graph are given by the set E. For a specific location of factories p1, . . . , pK , we can frame our task as solving the following optimization