Optimal Generation of Strictly Increasing Binary Trees and Beyond

TL;DR

This paper introduces two innovative algorithms for efficiently generating random increasing trees, including strictly increasing binary trees and weighted unary-binary increasing trees, enhancing randomness efficiency and algorithmic performance.

Contribution

The paper presents novel algorithms for generating increasing trees, improving efficiency and randomness usage over existing methods.

Findings

Efficient algorithm for strictly increasing binary trees.

Optimized recursive method for weighted unary-binary increasing trees.

Enhanced randomness utilization in tree generation algorithms.

Abstract

This article presents two novel algorithms for generating random increasing trees. The first algorithm efficiently generates strictly increasing binary trees using an ad hoc method. The second algorithm improves the recursive method for weighted strictly increasing unary-binary increasing trees, optimizing randomness usage.