Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present two algorithms for computing the geodesic distance beten phylogenetic trees in tree space, as introduced by Billera, Holmes, and Vogtmann [Adv. Appl. Math., 27 (2001), pp. 733-767].  show that the possible combinatorial types of shortest paths beten two trees can be compactly represented by a partially ordered set.  calculate the shortest distance along each candidate path by converting the problem into one of finding the shortest path through a certain region of Euclidean space. In particular,  show there is a linear time algorithm for finding the shortest path beten a point in the all-positive orthant and a point in the all-negative orthant of $\mathbb{R}^k$ contained in the subspace of $\mathbb{R}^k$ consisting of all orthants with the first $i$ coordinates nonpositive and the remaining coordinates nonnegative for $0 \leq i \leq k$.
['Megan Owen']
I am writing a research paper on a idea Computing Geodesic Distances in Tree Space
[{"from": "human", "value": "I am writing a research paper on a idea Computing Geodesic Distances in Tree Space"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present two algorithms for computing the geodesic distance beten phylogenetic trees in tree space, as introduced by Billera, Holmes, and Vogtmann [Adv. Appl. Math., 27 (2001), pp. 733-767].  show that the possible combinatorial types of shortest paths beten two trees can be compactly represented by a partially ordered set.  calculate the shortest distance along each candidate path by converting the problem into one of finding the shortest path through a certain region of Euclidean space. In particular,  show there is a linear time algorithm for finding the shortest path beten a point in the all-positive orthant and a point in the all-negative orthant of $\\mathbb{R}^k$ contained in the subspace of $\\mathbb{R}^k$ consisting of all orthants with the first $i$ coordinates nonpositive and the remaining coordinates nonnegative for $0 \\leq i \\leq k$."}]