2 papers
cs.CG2026
From Ham-Sandwich to Centerpoints: Semialgebraic Algorithms for Cutting Polytopal Measures
Marie-Charlotte Brandenburg, Jesús A. De Loera, Chiara Meroni
We design exact algorithms for the ham-sandwich and centerpoint theorems for polytopal measures. Our key observation is that the cap-volume function of such a measure, i.e., the vo…
math.OC2025
Approximation of starshaped sets using polynomials
Chiara Meroni, Jared Miller, Mauricio Velasco
We introduce polystar bodies: compact starshaped sets whose gauge or radial functions are expressible by polynomials, enabling tractable computations, such as that of intersection…