Computing min-convex hulls in the affine building of \(\mathrm{SL}_d\) (Q2022629)

Let \(K\) be a field with a discrete valuation. The author describes an algorithm for computing the min-convex hull of a finite collection of points in the affine building of the group SL\(_d (K)\). This min-convex hull can be realized as a tropical polytope, and the author's algorithm provides a bound for the dimension of the tropical projective space where this realization takes place. This is an improvement about other existing algorithms, and makes it feasible to compute min-convex hulls in practice for the first time.