Jia F. Weng

Canonical forms and algorithms for steiner trees in uniform orientation metrics

AbstractWe present some fundamental structural properties for minimum length networks (known as Steiner minimum trees) interconnecting a given set of points in an environment in which edge segments are restricted to λ uniformly oriented directions. We show that the edge segments of any full component of such a tree contain a total of at most four directions if λ is not a multiple of 3, or six directions if λ is a multiple of 3. This result allows us to develop useful canonical forms for these full components. The structural properties of these Steiner minimum trees are then used to resolve an important open problem in the area: does there exist a polynomial time algorithm for constructing a Steiner minimum tree if the topology of the tree is known? We obtain a simple linear time algorithm for constructing a Steiner minimum tree for any given set of points and a given Steiner topology.

Minimum Networks in Uniform Orientation Metrics

In this paper we use the variational method to systematically study properties of minimum networks connecting any given set of points (called terminals) in a

Compression Theorems and Steiner Ratios on Spheres

\lambda

On the Complexity of the Steiner Problem

-plane, in which all lines are in

Locally minimal uniformly oriented shortest networks

\lambda

Forbidden subpaths for Steiner minimum networks in uniform orientation metrics

uniform orientations

Maximum Parsimony, Substitution Model, and Probability Phylogenetic Trees

i\pi /\lambda\ (0\le i<\lambda )

A polynomial time algorithm for rectilinear Steiner trees with terminals constrained to curves

. We prove a number of angle conditions for Steiner minimum

Pseudo‐Gilbert–Steiner trees

\lambda

Expansion of Linear Steiner Trees

-trees, which are similar to the ones in the Euclidean case. In particular, we show that there exists a Steiner minimum