# Optimal Algorithm to Reconstruct a Tree from a Subtree Distance

## TL;DR

This paper presents a linear-time algorithm for reconstructing a tree from a subtree distance, extending the tree metric concept, and proves the uniqueness of the minimal representation.

## Contribution

It introduces a novel linear-time algorithm for reconstructing a tree from subtree distances and establishes the uniqueness of the minimal representation.

## Key findings

- The algorithm runs in linear time.
- The minimal representation of a subtree distance is unique.
- The method extends the tree metric concept.

## Abstract

This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time algorithm that finds such a representation. This algorithm achieves the optimal time complexity.