Uniformly branching trees

Steiner trees in uniformly quasi-bipartite graphs

The area of approximation algorithms for the Steiner tree problem in graphs has seen continuous progress over the last years. Currently the best approximation algorithm has a performance ratio of 1.550. This is still far away from 1.0074, the largest known lower bound on the achievable performance ratio. As all instances resulting from known lower bound reductions are uniformly quasi-bipartite,...

Fractal Trees with Side Branching

This paper considers fractal trees with self-similar side branching. The Tokunaga classification system for side branching is introduced, along with the Tokunaga self-similarity condition. Area filling (D = 2) and volume filling (D = 3) deterministic fractal tree constructions are introduced both with and without side branching. Applications to diffusion limited aggregation (DLA), actual draina...

Coupling on weighted branching trees

This paper considers linear functions constructed on two different weighted branching processes and provides explicit bounds for their Kantorovich-Rubinstein distance in terms of couplings of their corresponding generic branching vectors. Motivated by applications to the analysis of random graphs, we also consider a variation of the weighted branching process where the generic branching vector ...

Decision trees, boosted decision trees, branching programs, neural nets intro

Administrative: • Enrollment should be good now. • Next homework will go out next Wednesday or Friday. • Recap of where we are in course, and interplay between representation, optimization, and generalization; usual story is that as representation power improves, optimization and generalization become more painful. • Many basic latex errors in assignments; please consult lshort for an easy refe...

Branching Properties of Brownian Paths and Trees