# The Steiner distance problem for large vertex subsets in the hypercube

## TL;DR

This paper investigates the asymptotic behavior of the Steiner k-diameter in large hypercubes, providing new lower bounds through probabilistic methods to understand the complexity of large vertex subset distances.

## Contribution

The paper introduces a new lower bound for the Steiner k-diameter in hypercubes using probabilistic techniques, advancing understanding of large subset distances.

## Key findings

- Established asymptotic behavior of Steiner k-diameter for large k
- Developed a probabilistic method for lower bounds
- Enhanced understanding of hypercube vertex subset distances

## Abstract

We find the asymptotic behavior of the Steiner k-diameter of the $n$-cube if $k$ is large. Our main contribution is the lower bound, which utilizes the probabilistic method.