Corpus ID: 237940210

Tree balance indices: a comprehensive survey

@inproceedings{Fischer2021TreeBI,
  title={Tree balance indices: a comprehensive survey},
  author={Mareike Fischer and Lina Herbst and Sophie Kersting and Luise Kuhn and Kristina Wicke},
  year={2021}
}
Tree balance plays an important role in phylogenetics and other research areas, which is why several indices to measure tree balance have been introduced over the years. Nevertheless, a formal definition of what a balance index actually is and what makes it a useful measure of balance (or, in other cases, imbalance), has so far not been introduced in the literature. While the established indices all summarize the (im)balance of a tree in a single number, they vary in their definitions and… Expand
Explicit solution of divide-and-conquer dividing by a half recurrences with polynomial independent term
TLDR
This paper gives an explicit expression —in terms of the binary decomposition of n— for the solution xn of a recurrence of this form, with given initial condition x1, when the independent term p(n) is a polynomial in ⌈n/2⌉ and ⌊n/ 2⌋. Expand