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Shortest paths in treespace, which represent minimal deformations betweentrees, are unique and can be computed in polynomial time. The ability toquickly compute shortest paths has enabled new approaches for statisticalanalysis of populations of trees and phylogenetic inference. This paper gives anew algorithm for updating geodesic paths when the end points are dynamic. Suchalgorithms will be especially useful when optimizing for objectives that arefunctions of distances from a search point to other points e.g. for finding atree which has the minimum average distance to a collection of trees. Ourmethod for updating treespace shortest paths is based on parametric sensitivityanalysis of the maximum flow subproblems that are optimized when solving for atreespace geodesic.

Dynamic Geodesics in Treespace via Parametric Maximum Flow