L-Infinity Optimization to Bergman Fans of Matroids with an Application to Phylogenetics
L-Infinity Optimization to Bergman Fans of Matroids with an Application to Phylogenetics
Given a dissimilarity map $\delta$ on a finite set $X$, the set of ultrametrics (equidistant tree metrics) which are $l^\infty$-nearest to $\delta$ is a tropical polytope. We give an internal description of this tropical polytope which we use to derive a polynomial-time checkable test for the condition that all ultrametrics …