D. V. Feldman

Arranging convex bodies for maximum intersection volume: the sharp efficiency of centroid alignment

Given finitely many compact convex bodies in $\R^n$, one seeks translates maximizing the volume of their common intersection. A lazy solver merely translates each body so as to place its centroid at the origin. We prove that the lazy strategy always captures strictly more than $\left(\tfrac{2}{n+1}\right)^n$ of the opt...