# On a Subset Metric

## TL;DR

This paper introduces a new metric on finite subsets of a bounded metric space, extending previous subset distance concepts to facilitate error correction in DNA data storage and related applications.

## Contribution

It generalizes existing subset metrics, providing a new mathematical framework for analyzing error correction in subset-based data representations.

## Key findings

- Defines a new metric on finite subsets of a bounded metric space
- Extends the sequence-subset distance used in DNA data storage
- Builds on previous work by Eiter and Mannila on subset distance functions

## Abstract

For a bounded metric space X, we define a metric on the set of all finite subsets of X. This generalizes the sequence-subset distance introduced by Wentu Song, Kui Cai and Kees A. Schouhamer Immink to study error correcting codes for DNA based data storage. This work also complements the work of Eiter and Mannila where they study extensions of distance functions to subsets of a space in the context of various applications.